# Patent

## Title
Methods and systems for reducing acoustic echoes in communication systems

## Abstract

Various embodiments of the present invention are directed to methods and systems that reduce acoustic echoes in audio signals in accordance with changing conditions at first and second locations that are linked together in a communication system. In particular, one embodiment of the present invention relates to a method for determining an approximate impulse-response vector for canceling an acoustic echo resulting from an audio signal transmitted from the first location to the second location. This method includes forming a trust region within a search space based on computing a recursive specification vector defining the trust region. The method also includes computing a recursive shadow-impulse-response vector that lies substantially within the trust region, and computing the approximate impulse-response vector based on the recursive shadow-impulse-response vector and the recursive specification vector.

## Background
CROSS-REFERENCES TO RELATED APPLICATIONS
This application is a continuation-in-part of U.S. application Ser. No. 11/407,413, filed Apr. 20, 2006 now U.S. Pat. No. 8,045,730.


TECHNICAL FIELD
The present invention is related to acoustic echo cancellation, and, in particular, to methods and systems for reducing acoustic echoes in communication systems.
BACKGROUND OF THE INVENTION
Increasing interest in communication media, such as the Internet, electronic presentations, voice mail, and audio-conference communication systems, is increasing the demand for high-fidelity audio and communication technologies. Currently, individuals and businesses are using these communication media to increase efficiency and productivity, while decreasing cost and complexity. For example, audio-conference communication systems allow one or more individuals at a first location to simultaneously converse with one or more individuals at other locations through full-duplex communication lines in nearly real time, without wearing headsets or using handheld communication devices. Typically, audio-conference communication systems include a number of microphones and loudspeakers, at each location, that can be used by multiple individuals for sending and receiving audio signals to and from other locations.
In many audio-conference communication systems, audio signals carry a large amount of data, and employ a broad range of frequencies. Modern audio-conference communication systems attempt to provide clear transmission of audio signals, free from perceivable distortion, background noise, and other undesired audio artifacts. One common type of undesired audio artifact is an acoustic echo. Acoustic echoes can occur when a transmitted audio signal loops through an audio-conference communication system due to the coupling of microphones and speakers at a location. FIG. 1 shows a schematic diagram of an exemplary, two-location, audio-conference communication system. In FIG. 1, the audio-conference communication system 100 includes a near room 102 and a far room 104. Sounds, such as voices, produced in the near room 102 are detected by a microphone 106, and sounds produced in the far room 104 are detected by a microphone 108. The microphones 106 and 108 are transducers that convert the sounds into continuous analog signals that are represented by x(t) and y(t), respectively, where t is time.
The microphone 106 can detect many different sounds produced in the near room 102, including sounds output by the loudspeaker 114. An analog signal produced by the microphone 106 is represented by:

y(t)=s(t)+f(x(t))+v(t)

where

s(t) is an analog signal representing sounds produced in the near room 102,
v(t) is an analog signal representing noise, or extraneous signals created by disturbances in the microphone or communication channel 110, that, for example, may produces an annoying buzzing sound output from the loudspeaker 116, and
f(x(t)) is an analog signal that represents an acoustic echo.
The acoustic echo f(x(t)) is due to both acoustic propagation delay in the near room 102 and a round-trip transmission delay of the analog signal x(t) over the communication channels 110 and 112. Sounds generated by the analog signal y(t) are output from loudspeaker 116 in the far room 104. Depending on the amplification, or gain, in the amplitude of the signal y(t) and the magnitude of the acoustic echo f(x(t)), a person speaking into the microphone 108 in the far room 104 may also hear an annoying, high-pitched, howling sound emanating from loudspeaker 116 as a result of the sound generated by the acoustic echo f(x(t)).
Designers and manufacturers of audio-conference communication systems have attempted to compensate for acoustic echoes in various ways. One compensation technique employs a filtering system that reduces the acoustic echo. Typically, filtering systems employ adaptive filters that adapt to changing conditions at an audio-signal-receiving location. However, stand alone adaptive filters either fail to account for, or are often slow to adapt to, the widely varying acoustic path between loudspeaker and microphone. As a result, transmitted signals encoding conversations may be interrupted by numerous, brief periods of silence. Designers, manufacturers, and users of audio-conference communication systems have recognized a need for acoustic echo methods and systems that can reliably remove an acoustic echo from audio signals and that can rapidly adapt to the changing conditions at both audio-signal-receiving locations.
SUMMARY OF THE INVENTION
Various embodiments of the present invention are directed to methods and systems that reduce acoustic echoes in audio signals in accordance with changing conditions at first and second locations that are linked together in a communication system. In particular, one embodiment of the present invention relates to a method for determining an approximate impulse-response vector for canceling an acoustic echo resulting from an audio signal transmitted from the first location to the second location. This method includes forming a trust region within a search space based on computing a recursive specification vector defining the trust region. The method also includes computing a recursive shadow-impulse-response vector that lies substantially within the trust region, and computing the approximate impulse-response vector based on the recursive shadow-impulse-response vector and the recursive specification vector.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a schematic diagram of an exemplary, two-location, audio-conference communication system.
FIGS. 2A-2C illustrate conversion of an analog signal to a digital signal.
FIG. 3 is a plot of an impulse excitation of a loudspeaker and a plot of an overall room impulse response resulting at the output of the microphone in response to the impulse excitation.
FIGS. 4A-4D illustrate an example of determining a digital signal output from a microphone by convolving an input digital signal with the microphone impulse response.
FIG. 5 illustrates convolving a digital signal with a five-component impulse response in order to obtain a convolved digital signal.
FIG. 6 shows a schematic diagram of an exemplary, two-location, audio-conference communication system that includes an adaptive filter to reduce the level of the acoustic echo in the far room signal at the near room.
FIG. 7 illustrates convolving a digital signal with an impulse response in a frequency domain in order to obtain a time-domain, convolved digital signal.
FIG. 8 is an example plot of decision periods and decision epochs that represents an embodiment of the present invention.
FIG. 9 illustrates a two-location, audio-conference communication system that represents an embodiment of the present invention.
FIGS. 10A-10B show a control-flow diagram that represents an embodiment of the present invention for reducing acoustic echoes in audio signals that are transmitted from a first location to a second location.
FIGS. 10C-10D shows two plots of amplification energy versus time for the four types of control states that represents an embodiment of the present invention.
FIGS. 11A-11C is a control-flow diagram for a routine “determine control state” that is called in step 1008 of the control-flow diagram shown in FIG. 10A and that represents an embodiment of the present invention.
FIG. 12 is a control-flow diagram for a routine “residual echo suppression” that is called in step 1009 of the control-flow diagram shown in FIG. 10A and that represents an embodiment of the present invention.
FIG. 13A is a control-flow diagram for a routine “determine {right arrow over (ĥ)}(m)” that is called in step 1018 of the control-flow diagram shown in FIG. 10B and that represents an embodiment of the present invention.
FIG. 13B provides a two-dimensional representation of a hyper-elliptical region that represents an embodiment of the present invention.
FIG. 14 is a control-flow diagram for a routine “determine {right arrow over ({circumflex over (ε)})}(m)” that is called in step 1304 of the control-flow diagram shown in FIG. 13 and that represents an embodiment of the present invention.
FIG. 15 is a control-flow diagram for a routine “determine μm” that is called in step 1306 of the control-flow diagram shown in FIG. 13 and that represents an embodiment of the present invention.
FIG. 16 is a control-flow diagram for a routine “determine γm” that is called in step 1307 of the control-flow diagram shown in FIG. 13 and that represents an embodiment of the present invention.



DETAILED DESCRIPTION OF THE INVENTION
Various embodiments of the present invention are directed to methods and systems that reduce acoustic echoes in audio signals in accordance with changing conditions at first and second locations that are linked together in a communication system. The terms “first location” and “second location” are broad general terms that are associated with the different locations of the near room and the far room, respectively, which are used to describe below various method embodiments of the present invention. The communication system can be the Internet, electronic presentations, voice mail, audio-conference communication systems or any other kind of communication system that transmits signals between a first location and a second location. In various embodiments of the present invention, a first digital signal and a second digital signal are received as input at the first location. The first digital signal encodes sounds produced at a first location. The second digital signal encodes an acoustic echo and sounds produced at the second location. The methods compute a control state that depends on the state of current signal transmission. The control state represents one of the following: (1) sound transmitted from the first location only; (2) sound transmitted from the second location only; (3) sounds transmitted simultaneously between the first and second locations; and (4) no sound transmitted between the first and second locations. The methods then compute an approximate acoustic echo based on the control state. The methods generate an output digital signal at the first location by first subtracting the computed, approximate acoustic echo from the second digital signal, then adjusting the second digital signal for gain based on the control state. Finally, the output digital signal is transmitted to the first location.
In order to assist in understanding descriptions of various embodiments of the present invention, an overview of digital signals, impulse responses, and convolution is provided in a first subsection. An overview of acoustic echo cancellation is provided in a second subsection. An overview of discrete Fourier transformations is provided in a third subsection. Embodiments of the present invention are provided in a fourth subsection.
An Overview of Digital Signals, Impulse Responses, and Convolution
Sounds received by a microphone are transformed into an analog signal comprising a time-dependent, continuously varying voltage. In order to process an analog signal using a digital computer, the analog signal is first converted into a digital signal with minimal alteration of the essential information contained in the analog signal. Digital signals can be stored electronically, magnetically, or optically and can be processed using logical operations encoded in computer programs.
FIGS. 2A-2C illustrate conversion of an analog signal into a digital signal. In FIGS. 2A-2B, horizontal axes, such as horizontal axis 202, represent time, and vertical axes, such as vertical axis 204, represent analog signal amplitudes in volts. FIG. 2A is a plot of a time-dependent, continuously-varying analog signal x(t) 206. The analog signal x(t) 206 is first sampled by measuring the amplitude of the analog signal x(t) at discrete sampling times. In order to prevent loss of essential information contained in the analog signal, the duration between sampling times is generally selected to be sufficiently short so that the analog signal varies little between consecutive sampling times. FIG. 2B is a plot of a sampled signal 208 obtained by sampling the analog signal 206 in FIG. 2A. The sampling times are in tenths of a second, and the sampled signal 208 is approximated as a step function by assuming a constant-signal amplitude between sampling times. For example, a constant-amplitude region 210 represents a constant value of −1.9 volts between sampling times 0.2 and 0.3 seconds.
For efficient and convenient digital signal processing, it is desirable for both time and magnitude values to be integers. Therefore, an integer-encoded, digital signal is produced by multiplying the value of each constant-amplitude region by a selected constant and by multiplying the sampling times by a selected constant in order to produce integer values that represent the amplitude and sampling times of each step in the step function. An integer-valued sampling time is called a “time sample,” and an integer-valued amplitude is called a “digital amplitude.” The resulting digital signal can be functionally represented by x[n], where n, an independent variable, represents a time sample domain. FIG. 2C is a plot of a digital signal obtained from the sampled signal 208 in FIG. 2B. In FIG. 2C, horizontal axis 212 is a time sample domain, vertical axis 214 is a digital signal axis. Each point in the graph represents a quantized value representing the scaled amplitude of the digital signal at a scaled sampling time. For example, point x[2] 216 with coordinates (2, −19) represents step 210 in FIG. 2B.
A digital signal x[n] can, in general, be thought of as a series of impulses, each impulse corresponding to a unique component. The notation x[n], where n represents a particular time sample, can also be used to represent a single impulse of a digital signal that is called a “component” of a signal. Each component is a signal comprising all zero sample values except for a single value representing the amplitude at a single time sample, and is mathematically represented by:

x[n]=dδ[n−p]

where

d is an integer scale factor that represents the amplitude, or strength, of the impulse,
p is a time sample, and
δ is the delta function defined as:




  
    δ
    ⁡
    
      [
      
        n
        -
        p
      
      ]
    
  
  =
  
    {
    
      
        
          1
        
        
          
            
              when
              ⁢
              
                
              
              ⁢
              n
            
            =
            p
          
        
      
      
        
          0
        
        
          otherwise
        
      
    
  




For example, in FIG. 2C, the component x[0] 218 is equal to 10δ[p], and the component x[2] 216 is equal to ·19δ[2−p]. In other words, p in the delta function δ[n−p] represents a time sample shift, and n−p represents a time sample relative to time sample n.

A digital impulse response, h[n], is a digital signal that is output from a microphone when the input to the microphone is a unit impulse δ[n], where p is “0” and d equals “1.” The impulse response of a microphone can be determined by applying an impulse of sound with a very short duration to the microphone and measuring the signal output by the microphone. The impulse response can also be represented by a vector as follows:




  
    h
    ⁡
    
      [
      n
      ]
    
  
  =
  
    
      
        h
        _
      
      n
    
    =
    
      [
      
        
          
            
              
                h
                n
              
              ⁡
              
                [
                0
                ]
              
            
          
        
        
          
            
              
                h
                n
              
              ⁡
              
                [
                1
                ]
              
            
          
        
        
          
            ⋮
          
        
        
          
            
              
                h
                n
              
              ⁡
              
                [
                
                  L
                  -
                  1
                
                ]
              
            
          
        
      
      ]
    
  




where hn[·] is an impulse response component, and

L is the number of components that together compose the impulse response.
FIG. 3 shows a plot of an impulse x[n] and a plot of an overall room impulse response h[n] produced in response to the impulse x[n]. The impulse response h[n] includes the loudspeaker, room, and microphone. In FIG. 3, impulse plot 302 represents an impulse x[n] input to a hypothetical microphone 304. The impulse x[n] 302 comprises all zeros except for a single nonzero point 306 at n equal to 0 and is represented by dδ[n−p] as described above. In this case, d equals “1” and p equals “0” so the impulse can be represented as δ[n]. In response to the impulse 302, the microphone 304 outputs an impulse response h[n] that is represented by an impulse-response plot 308. The impulse response 308 comprises all zeros except for the three nonzero digital signals represented by points 310-312. An actual digital impulse response to an impulse typically comprises a greater number of nonzero components than contained in the impulse, as shown in FIG. 3. For example, the impulse response 308 includes 3 nonzero components while impulse 302 includes a single nonzero component. Impulse response 308 can be represented by the 3-component vector:




  
    h
    ⁡
    
      [
      0
      ]
    
  
  =
  
    
      
        h
        _
      
      0
    
    =
    
      
        [
        
          
            
              
                
                  h
                  0
                
                ⁡
                
                  [
                  0
                  ]
                
              
            
          
          
            
              
                
                  h
                  0
                
                ⁡
                
                  [
                  1
                  ]
                
              
            
          
          
            
              
                
                  h
                  0
                
                ⁡
                
                  [
                  2
                  ]
                
              
            
          
        
        ]
      
      =
      
        [
        
          
            
              1
            
          
          
            
              
                -
                1
              
            
          
          
            
              
                -
                .25
              
            
          
        
        ]
      
    
  




Typically, the impulse used to determine an impulse response is output from a loudspeaker into a room and is detected by a microphone. The loudspeaker, room, and microphone are referred to as a “system,” and an associated impulse response can be thought of as a system impulse response. A digital signal transmitted from the system is determined by convolving a digital signal x[n] produced by the system with the impulse response h[n] of the system. The convolved digital signal is represented by xc[n]. FIGS. 4A-4D provide a graphical example of convolving a three-component digital signal x[n] produced by a hypothetical system with an impulse response h[n] in order to produce a digital signal xc[n] output from the system. FIG. 4A is a plot of an example, two-component, impulse response h[n] 402 that is produced by the hypothetical system. The impulse response h[n] is assumed to be invariant with time.
FIG. 4B is a plot of a first component of the digital signal x[n] that is input to the system at a time sample “0.” The first component is represented by a scaled impulse 2δ[0] 404. In response to the impulse 2δ[n] 404, the system outputs an impulse-response h[n] comprising a first component 406 at the time sample “0,” and outputs a second component 408 at a later time sample “1.” The impulse response to the impulse 2δ[n] 404 is essentially the impulse response in FIG. 4A with the components multiplied by the impulse scale factor “2.”
FIG. 4C is a plot of a second component of the digital signal x[n] that is input to the system at the later time sample “1.” The second component is represented by an impulse δ[n−1] 410. In response to the impulse δ[n−1] 410, the system outputs an impulse-response comprising a third component 412 at the time sample “1,” and outputs a fourth component 414 at a later time sample “2.” The impulse response to the impulse δ[n−1] 410 is essentially the impulse response in FIG. 4A with the component time samples shifted by a factor of “1.” Because the second and the third components 408 and 412 occur at the same time sample “1,” the amplitudes of the components 408 and 412 are summed in order to obtain a fifth component 416, which is the output at the time sample “1.”
FIG. 4D is a plot of a third component of the digital signal x[n] that is input to the system at the time sample “2.” The second component is represented by an impulse −2δ[n−2] 418. In response to the impulse −2δ[n−2], the system outputs an impulse response comprising a sixth component 420 at the time sample “2,” and a seventh component 422 at a later time sample “3.” The impulse response to the impulse −2[n−2] 418 is essentially the impulse response in FIG. 4A with the components multiplied by the scale factor “−2,” and the component time samples shifted by a factor of “2.” Because the fifth and the sixth components 414 and 420 occur at the same time sample “2,” the amplitudes of the component 414 and 420 are summed to give an eighth component 424, which is the output at the time sample “2.”
Note that convolving the three-component, input digital signal x[n] with the two-component impulse response h[n] outputs the four-component digital signal xc[n]. In general, convolving an N component input digital signal x[n] with an L component impulse response h[n] gives an N+L−1 component output signal xc[n].
Components of the convolved digital signal xc[n] 426, in FIG. 4D, can also be obtained by calculating the scalar product of a two-component vector representation of the impulse response and two-component vectors corresponding to each component of the digital signal x[n] that are given by:




  
    
      h
      _
    
    =
    
      
        [
        
          
            
              
                h
                ⁡
                
                  [
                  0
                  ]
                
              
            
          
          
            
              
                h
                ⁡
                
                  [
                  1
                  ]
                
              
            
          
        
        ]
      
      =
      
        [
        
          
            
              1
            
          
          
            
              
                -
                1
              
            
          
        
        ]
      
    
  
  ,
  
    
      and
      ⁢
      
        
      
      ⁢
      
        
          x
          _
        
        ⁡
        
          [
          n
          ]
        
      
    
    =
    
      [
      
        
          
            
              x
              ⁡
              
                [
                n
                ]
              
            
          
        
        
          
            
              x
              ⁡
              
                [
                
                  n
                  -
                  1
                
                ]
              
            
          
        
      
      ]
    
  




The order of the components in the column vectors {right arrow over (h)} and {right arrow over (x)}[n] are opposite in time ordering with respect to one another. For example, in the column vector {right arrow over (h)}, the first component h[0] appears earlier in time than the second component h[1], while, in the column vector {right arrow over (x)}[n], the first component x[n] appears later in time than the second component x[n−1]. Note that components of the vector {right arrow over (x)}[n] that correspond to negative valued time samples are assigned the value “0.” For example, the first component 406, in FIG. 4D, is calculated by:





  
    
      x
      c
    
    ⁡
    
      [
      0
      ]
    
  
  =
  
    
      
        
          [
          
            
              h
              ⁡
              
                [
                0
                ]
              
            
            ,
            
              h
              ⁡
              
                [
                1
                ]
              
            
          
          ]
        
        T
      
      ⁢
      
        
      
      [
      
        
          
            
              x
              ⁡
              
                [
                0
                ]
              
            
          
        
        
          
            
              x
              ⁡
              
                [
                
                  -
                  1
                
                ]
              
            
          
        
      
      ]
    
    =
    
      
        
          
            [
            
              1
              ,
              
                -
                1
              
            
            ]
          
          T
        
        ⁡
        
          [
          
            
              
                2
              
            
            
              
                0
              
            
          
          ]
        
      
      =
      2
    
  




where the component x[−1] is assigned the value “0.” The second, third, and fourth components 416, 424, and 422 are calculated by:




  
    
      
        
          x
          c
        
        ⁡
        
          [
          1
          ]
        
      
      =
      
        
          
            
              [
              
                
                  h
                  ⁡
                  
                    [
                    0
                    ]
                  
                
                ,
                
                  h
                  ⁡
                  
                    [
                    1
                    ]
                  
                
              
              ]
            
            T
          
          ⁢
          
            
          
          [
          
            
              
                
                  x
                  ⁡
                  
                    [
                    1
                    ]
                  
                
              
            
            
              
                
                  x
                  ⁡
                  
                    [
                    0
                    ]
                  
                
              
            
          
          ]
        
        =
        
          
            
              
                [
                
                  1
                  ,
                  
                    -
                    1
                  
                
                ]
              
              T
            
            ⁡
            
              [
              
                
                  
                    1
                  
                
                
                  
                    2
                  
                
              
              ]
            
          
          =
          
            -
            1
          
        
      
    
    ,
    
      

    
    ⁢
    
      
        
          x
          c
        
        ⁡
        
          [
          2
          ]
        
      
      =
      
        
          
            
              [
              
                
                  h
                  ⁡
                  
                    [
                    0
                    ]
                  
                
                ,
                
                  h
                  ⁡
                  
                    [
                    1
                    ]
                  
                
              
              ]
            
            T
          
          ⁢
          
            
          
          [
          
            
              
                
                  x
                  ⁡
                  
                    [
                    2
                    ]
                  
                
              
            
            
              
                
                  x
                  ⁡
                  
                    [
                    1
                    ]
                  
                
              
            
          
          ]
        
        =
        
          
            
              
                [
                
                  1
                  ,
                  
                    -
                    1
                  
                
                ]
              
              T
            
            ⁡
            
              [
              
                
                  
                    
                      -
                      2
                    
                  
                
                
                  
                    1
                  
                
              
              ]
            
          
          =
          
            -
            3
          
        
      
    
    ,
    and
  




  
    
      
        
          x
          c
        
        ⁡
        
          [
          3
          ]
        
      
      =
      
        
          
            
              [
              
                
                  h
                  ⁡
                  
                    [
                    0
                    ]
                  
                
                ,
                
                  h
                  ⁡
                  
                    [
                    1
                    ]
                  
                
              
              ]
            
            T
          
          ⁢
          
            
          
          [
          
            
              
                
                  x
                  ⁡
                  
                    [
                    3
                    ]
                  
                
              
            
            
              
                
                  x
                  ⁡
                  
                    [
                    2
                    ]
                  
                
              
            
          
          ]
        
        =
        
          
            
              
                [
                
                  1
                  ,
                  
                    -
                    1
                  
                
                ]
              
              T
            
            ⁡
            
              [
              
                
                  
                    0
                  
                
                
                  
                    
                      -
                      2
                    
                  
                
              
              ]
            
          
          =
          2
        
      
    
    ,
  



respectively.

In general, a component of a convolved digital signal xc[n] is mathematically determined by:




  
    
      
        
          
            x
            c
          
          ⁡
          
            [
            n
            ]
          
        
        =
        
          
            x
            ⁡
            
              [
              n
              ]
            
          
          *
          
            h
            ⁡
            
              [
              n
              ]
            
          
        
      
    
  
  
    
      
        =
        
          
            
              h
              _
            
            n
          
          ·
          
            
              x
              _
            
            ⁡
            
              [
              n
              ]
            
          
        
      
    
  
  
    
      
        =
        
          
            ∑
            
              i
              =
              0
            
            
              L
              -
              1
            
          
          ⁢
          
            
              
                h
                n
              
              ⁡
              
                [
                i
                ]
              
            
            ⁢
            
              x
              ⁡
              
                [
                
                  n
                  -
                  i
                
                ]
              
            
          
        
      
    
  




where

“*” is a symbol that represents convolution, and




  
    
      x
      _
    
    ⁡
    
      [
      n
      ]
    
  
  =
  
    [
    
      
        
          
            x
            ⁡
            
              [
              n
              ]
            
          
        
      
      
        
          
            x
            ⁡
            
              [
              
                n
                -
                1
              
              ]
            
          
        
      
      
        
          ⋮
        
      
      
        
          
            x
            ⁡
            
              [
              
                n
                -
                
                  (
                  
                    L
                    -
                    1
                  
                  )
                
              
              ]
            
          
        
      
    
    ]
  




In order to compute a convolved signal component xc[n], the L previously obtain digital signal components of the digital signal x[n] are used, and the components of the vector {right arrow over (x)}[n] that correspond to negative valued time samples are assigned the value “0.”

FIG. 5 illustrates convolving a digital signal displayed in plot 502 with a five-component impulse response in order to obtain a convolved digital signal displayed in plot 504. In plots 502 and 504, horizontal axes, such as horizontal axis 506, are time sample axes, and vertical axes, such as vertical axis 508, are digital number axes. The convolved digital signal sample 510 in plot 504 is obtained as shown in FIG. 5 and is mathematically represented by:




  
    
      
        
          
            x
            c
          
          ⁡
          
            [
            n
            ]
          
        
        =
        
          
            x
            ⁡
            
              [
              n
              ]
            
          
          *
          
            h
            ⁡
            
              [
              n
              ]
            
          
        
      
    
  
  
    
      
        =
        
          
            
              [
              
                
                  
                    
                      
                        h
                        n
                      
                      ⁡
                      
                        [
                        0
                        ]
                      
                    
                  
                  
                    
                      
                        h
                        n
                      
                      ⁡
                      
                        [
                        1
                        ]
                      
                    
                  
                  
                    
                      
                        h
                        n
                      
                      ⁡
                      
                        [
                        2
                        ]
                      
                    
                  
                  
                    
                      
                        h
                        n
                      
                      ⁡
                      
                        [
                        3
                        ]
                      
                    
                  
                  
                    
                      
                        h
                        n
                      
                      ⁡
                      
                        [
                        4
                        ]
                      
                    
                  
                
              
              ]
            
            T
          
          ⁡
          
            [
            
              
                
                  
                    x
                    ⁡
                    
                      [
                      n
                      ]
                    
                  
                
              
              
                
                  
                    x
                    ⁡
                    
                      [
                      
                        n
                        -
                        1
                      
                      ]
                    
                  
                
              
              
                
                  
                    x
                    ⁡
                    
                      [
                      
                        n
                        -
                        2
                      
                      ]
                    
                  
                
              
              
                
                  
                    x
                    ⁡
                    
                      [
                      
                        n
                        -
                        3
                      
                      ]
                    
                  
                
              
              
                
                  
                    x
                    ⁡
                    
                      [
                      
                        n
                        -
                        4
                      
                      ]
                    
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        =
        
          
            ∑
            
              i
              =
              0
            
            4
          
          ⁢
          
            
              
                h
                n
              
              ⁡
              
                [
                i
                ]
              
            
            ⁢
            
              x
              ⁡
              
                [
                
                  n
                  -
                  i
                
                ]
              
            
          
        
      
    
  




where superscript T identifies the matrix transpose operation.

In the examples of convolution described above, the impulse response is assumed to remain constant at each time sample in the time domain. However, in practice, the impulse response of a system often depends on the conditions of the room. In other words, the impulse response of the system may change over time as conditions in the room change. For example, an impulse response of a system with no sound produced in the room is different from an impulse response of the same system at a later time when sounds are produced in the room.
An Overview of Acoustic Echo Cancellation
FIG. 6 shows a schematic diagram of the exemplary, two-location, audio-conference communication system shown in FIG. 1 that includes an adaptive filter 602 to reduce the level of an acoustic echo in the far room 104 at the near room 102. In FIG. 6, the digital signal x[n] is transmitted in the communication channel 112 from the far room 104 to the loudspeaker 114 in the near room 102. When the digital signal x[n] reaches the loudspeaker 114, the digital signal x[n] can be converted back into an analog signal x(t) and sound is output from the loudspeaker 114. The microphone 106 detects the sound output from the loudspeaker 114 and any sounds produced in the near room 102. The microphone outputs a digital signal in the communication channel 110 to the far room 104 that is mathematically represented by:

y[n]=s[n]+xc[n]+v[n]

where

xc[n]=x[n]*h[n] is a convolved digital signal that represents an acoustic echo and is produced by convolving the digital signal x[n] with the impulse response h[n] of the microphone 106,
s[n] is a digital signal that represents sounds produced in the near room 102, and
v[n] is a digital signal that represents any noise produced by electrical disturbances in both the microphone 106 and the communications channel 110.
In practice, the impulse response h[n] of the microphone 106 is not known with certainty. In order to reduce the amount of the acoustic echo xc[n] present in the digital signal y[n], an approximate acoustic echo is subtracted from the digital signal y[n]. The approximate acoustic echo is produced by also transmitting the digital signal x[n] to an adaptive filter 602, which produces an approximate impulse response, ĥ[n]. The adaptive filter 602 convolves the approximate impulse response ĥ[n] with the digital signal x[n], in order to produce the approximate acoustic echo x[n]*ĥ[n], which is subtracted from the digital signal y[n] at the summing junction 604. Subtracting the approximate acoustic echo x[n]*ĥ[n] at the summing junction 604 gives an output digital signal that is mathematically represented by:




  
    
      
        
          
            r
            ^
          
          ⁡
          
            [
            n
            ]
          
        
        =
        
        ⁢
        
          
            y
            ⁡
            
              [
              n
              ]
            
          
          -
          
            
              x
              ⁡
              
                [
                n
                ]
              
            
            *
            
              
                h
                ^
              
              ⁡
              
                [
                n
                ]
              
            
          
        
      
    
  
  
    
      
        =
        
        ⁢
        
          
            s
            ⁡
            
              [
              n
              ]
            
          
          +
          
            (
            
              
                
                  x
                  ⁡
                  
                    [
                    n
                    ]
                  
                
                *
                
                  h
                  ⁡
                  
                    [
                    n
                    ]
                  
                
              
              -
              
                
                  x
                  ⁡
                  
                    [
                    n
                    ]
                  
                
                *
                
                  
                    h
                    ^
                  
                  ⁡
                  
                    [
                    n
                    ]
                  
                
              
            
            )
          
          +
          
            v
            ⁡
            
              [
              n
              ]
            
          
        
      
    
  
  
    
      
        ≅
        
        ⁢
        
          
            s
            ⁡
            
              [
              n
              ]
            
          
          +
          
            v
            ⁡
            
              [
              n
              ]
            
          
        
      
    
  




where

x[n]*h[n]−x[n]*ĥ[n] is called the “residual echo.”
The residual echo is a portion of the digital signal y[n] that is transmitted to the far room 104. Acoustic echo cancellation methods and systems are directed to producing approximate acoustic echoes that make the residual echoes inaudible to individuals that are simultaneously producing sounds input to the microphone 108 and listening to the loudspeaker 116 in the far room 104. The adaptive filter 602 is used to reduce the acoustic echo transmitted from the near room 102 to the far room 104. However, in practice, a second adaptive filter is needed to reduce an acoustic echo transmitted from the far room 104 to the near room 102.
An Overview of Discrete Fourier Transforms
Convolving a digital signal x[n] with an impulse response h[n] is often a computationally time-consuming step in the determination of an output digital signal {circumflex over (r)}[n]. However, the computational time devoted to convolution can often be reduced by first separately mapping the digital signals x[n] and h[n] to discrete frequency domain digital signals X[k] and H[k], respectively, using a discrete Fourier transform (“DFT”). The DFT is given by:




  
    X
    ⁡
    
      [
      k
      ]
    
  
  =
  
    
      1
      L
    
    ⁢
    
      
        ∑
        
          n
          =
          0
        
        
          L
          -
          1
        
      
      ⁢
      
        
          x
          ⁡
          
            [
            n
            ]
          
        
        ⁢
        
          exp
          ⁡
          
            (
            
              
                
                  -
                  j
                
                ⁢
                
                  
                
                ⁢
                2
                ⁢
                
                  
                
                ⁢
                π
                ⁢
                
                  
                
                ⁢
                kn
              
              L
            
            )
          
        
      
    
  




where k is an inverse time sample index with the units of inverse time or frequency, and

j=√{square root over (−1)}.

Next, the digital signals X[k] and H[k] are multiplied in the frequency domain and an inverse discrete Fourier transformation (“IDFT”) is applied to the product X[k]H[k], in order to obtain the convolved digital signal x[n]*h[n]. The IDFT applied to the product X[k]H [k] is:





  
    
      x
      ⁡
      
        [
        n
        ]
      
    
    *
    
      h
      ⁡
      
        [
        n
        ]
      
    
  
  =
  
    
      ∑
      
        k
        =
        0
      
      
        N
        -
        1
      
    
    ⁢
    
      
        X
        ⁡
        
          [
          k
          ]
        
      
      ⁢
      
        H
        ⁡
        
          [
          k
          ]
        
      
      ⁢
      
        
      
      ⁢
      exp
      ⁢
      
        
      
      ⁢
      
        (
        
          
            j
            ⁢
            
              
            
            ⁢
            2
            ⁢
            π
            ⁢
            
              
            
            ⁢
            kn
          
          N
        
        )
      
    
  




where N is the number of digital signals in the inverse time sample domain.

FIG. 7 illustrates convolution of the digital signals x[n] and h[n] by first mapping the digital signals x[n] and h[n] to the frequency domain and mapping the product X[k]H[k] back to the time sample domain in order to obtain convolved digital signal x[n]*h[n]. In FIG. 7, directional arrow 702 represents applying a discrete Fourier transform (“DFT”) to the digital signal x[n] in order to obtain a digital signal X[k], and directional arrow 704 represents applying the DFT to the impulse response h[n] in order to obtain a digital signal H[k]. The digital signals X[k] and H[k] are multiplied in the frequency domain in order to obtain the product X[k]H[k]. Next, an IDFT 706 is applied the product X[k]H[k] in order to obtain the convolved digital signal x[n]*h[n].
A fast Fourier transformation (“FFT”) and a corresponding inverse fast Fourier transform (“IFFT”) are types of Fourier transformations that are often employed in order to avoid carrying out convolution in the time sample domain. Using the FFT and the IFFT can be hundreds or even thousands of times faster than convolving digital signals in the time domain. A number of different FFT and IFFT methods are described in the book “Discrete-Time Signal Processing (2nd Edition),” by A. Oppenhiemer, R. Schafer, and J. Buck, Prentice Hall, Inc., (1999-2000), which is just one of many references for the field of digital signal processing. Additional details can be obtained from the above-referenced book, or from many other textbooks, papers, and journal articles in this field.
EMBODIMENTS OF THE PRESENT INVENTION
Various embodiments of the present invention are directed to methods and systems that reduce acoustic echoes in audio signals and in accordance with changing conditions at separate locations linked by an audio-conference communication systems. In particular, embodiments of the present invention include methods for determining an approximate impulse-response vector corresponding to audio signals transmitted only from the far room to the near room, methods for canceling an acoustic echo produced during substantially simultaneous transmission of audio signals from the near room to the far room, and methods for updating a data structure used to store a number of approximate impulse-response vectors.
Various embodiments of the present invention are mathematical in nature. For this reason, method embodiments of the present invention are described below with reference to numerous equations, and with reference to graphical illustrations and control-flow diagrams.
I. An Overview of Mathematical Foundations that Relate to Embodiments of the Present Invention
The various embodiments of the present invention are based on a decision-making framework comprising Markov decision processes, sequential optimization, and optimal control theory. Two references for these fields are the books “Markov Decision Processes: Discrete Stochastic Dynamic Programming,” by M. L. Puterman, John Wiley and Sons, New York, 1994; and “Dynamic Programming and Optimal Control,” by D. P. Bertsekas, Athena Scientific vol. I and II, Belmont, Mass., 1995. The description below presents those elements of Markov decision processes and the elements of optimal control theory that relate to embodiments of the present invention. Additional details can be obtained from the above-referenced books, or from many other books, papers, and journal articles in these fields.
As described above with reference to FIG. 3, an impulse response h[n] of a microphone can be mathematically represented as an L-component vector {right arrow over (h)}n. A property of the impulse response is that:

{right arrow over (h)}nε⊂L 

where

L is an L-dimensional vector space,
 is a set centered at the origin in L with a radius of √{square root over (E)}, and
E represents the maximum amplification energy, or gain, produced by a microphone in response to an impulse.
In other words, the Euclidean norm of each impulse response output from a microphone satisfies the condition:




  
    
    
      
        h
        →
      
      n
    
    
  
  =
  
    
      
        
          ∑
          
            i
            =
            0
          
          
            L
            -
            1
          
        
        ⁢
        
          
            (
            
              
                h
                n
              
              ⁡
              
                [
                i
                ]
              
            
            )
          
          2
        
      
    
    <
    
      2
      ⁢
      
        E
      
    
  




Although, in practice, an impulse response {right arrow over (h)}n is not known with certainty during acoustic echo cancellation, methods of the present invention are based on obtaining an approximate impulse response {right arrow over (ĥ)}n that minimizes the average error:

Jhn({circumflex over (h)})=∫(y[n]−{right arrow over (ĥ)}n·{right arrow over (x)}[n])2dPhn 

where

(y[n]−{right arrow over (ĥ)}n·{right arrow over (x)}[n])2 is the error between the digital signal y[n] and the acoustic echo {right arrow over (h)}nT·{right arrow over (x)}[n], and
Phn is a joint probability distribution function associated with the error (y[n]−{right arrow over (ĥ)}n·{right arrow over (x)}[n])2.
The average error Jhn(ĥ) can also be thought of as an expectation value of a random variable (y[n]−{right arrow over (ĥ)}n·{right arrow over (x)}[n])2 with an associated probability Phn.
The method of the present invention produces approximate impulse responses {right arrow over (ĥ)}n that minimize the average error Jhn({right arrow over (ĥ)}n) and satisfy the following condition:




  
    
    
      
        
          h
          →
        
        n
      
      -
      
        
          h
          
            _
            ^
          
        
        n
      
    
    
  
  =
  
    inf
    ⁢
    
      
    
    ⁢
    
      {
      
        
          
            
            
              
                
                  h
                  _
                
                n
              
              -
              
                
                  h
                  
                    _
                    ^
                  
                
                n
              
            
            
          
          ⁢
          
            :
          
          ⁢
          
            
          
          ⁢
          
            
              h
              
                _
                ^
              
            
            n
          
        
        ∈
        
          
            H
            
              ɛ
              n
            
          
          ⁡
          
            (
            
              
                h
                
                  _
                  ^
                
              
              n
            
            )
          
        
      
      }
    
  




where




  
    
      
        
        
          
            
              h
              →
            
            n
          
          -
          
            
              h
              
                _
                ^
              
            
            n
          
        
        
      
      =
      
        
          
            ∑
            
              i
              =
              1
            
            L
          
          ⁢
          
            
              (
              
                
                  
                    h
                    n
                  
                  ⁡
                  
                    [
                    i
                    ]
                  
                
                -
                
                  
                    
                      h
                      ^
                    
                    n
                  
                  ⁡
                  
                    [
                    i
                    ]
                  
                
              
              )
            
            2
          
        
      
    
    ,
    
      

    
    ⁢
    and
  




  
    
      
        H
        
          ɛ
          n
        
      
      ⁡
      
        (
        
          
            h
            
              _
              ^
            
          
          n
        
        )
      
    
    =
    
      {
      
        
          
            h
            
              _
              ^
            
          
          n
        
        ∈
        
          
            U
            ⁢
            
              :
            
            ⁢
            
              
            
            ⁢
            
              
                J
                
                  h
                  n
                
              
              ⁡
              
                (
                
                  h
                  
                    _
                    ^
                  
                
                )
              
            
          
          <
          
            
              
                σ
                z
                2
              
              ⁡
              
                (
                n
                )
              
            
            +
            
              
                ɛ
                n
              
              ⁢
              
                
                  σ
                  x
                  2
                
                ⁡
                
                  (
                  n
                  )
                
              
              ⁢
              E
            
          
        
      
      }
    
  



In the set εn({right arrow over (ĥ)}n),  is a set centered at the origin in L with a radius of √{square root over (E)} and is called a “search space,” εn is a subjectively small positive real number,




  
    
      
        σ
        z
        2
      
      ⁡
      
        (
        n
        )
      
    
    =
    
      
        inf
        
          
            
              h
              ^
            
            n
          
          ∈
          U
        
      
      ⁢
      
        
          J
          
            h
            n
          
        
        ⁡
        
          (
          
            h
            
              _
              ^
            
          
          )
        
      
    
  
  ,




and σ{right arrow over (x)}2 (n)=∫∥{right arrow over (x)}[n]∥2dPhn is the variance of the digital signal vector {right arrow over (x)}[n]. The symbol “inf” means the “infimum,” which is the maximum lower bound of a set. For example, the infimum of the open interval (0,1) is the number “0” and is represented by inf(0,1)=0 even though the number “0” is not an element of the open interval (0,1).

II. A Stochastic Approximation of the Approximate Impulse Response {right arrow over (ĥ)}n 

The method of the present invention is also based on the assumption that an impulse response {right arrow over (h)}n exhibits little variation over Nc time samples, and the maximum deviation between Nc time samples is bounded by:

∥{right arrow over (h)}n−{right arrow over (h)}n+Nc∥≦2√{square root over (E)}

The parameter Nc is called the “coherence time.” As a result, rather than determine an approximate impulse response {right arrow over (ĥ)}n for each time sample n, an approximate impulse response, {right arrow over (ĥ)}m, is determined at the beginning of every Nd time samples, where Nd<<Nc, and m is a positive integer. An interval with Nd time samples is called a “decision period,” and the beginning of a decision period is called a “decision epoch.”

FIG. 8 is an example plot of decision periods and decision epochs associated with impulse-response vectors that represents an embodiment of the present invention. In FIG. 8, horizontal axis 802 is a time sample axis, vertical axis 804 is digital number axis, and dots, such as dot 806, represent a digital signal x[n]. Decision periods 808, 810, and 812 are each comprised of six time samples (Nd=6). Decision epochs occur at the beginning of the decision periods 808, 810, and 812. Embodiments of the present invention described below produce a new approximate impulse response {right arrow over (ĥ)}m at each decision epoch. For example, at the beginning of the decision period 808, an initial approximate impulse response {right arrow over (ĥ)}1 is provided. At the beginning of the decision period 810, a new approximate impulse response {right arrow over (ĥ)}2 is computed. In general, at the beginning of a decision period (m−1)Nd 812, an approximate impulse response {right arrow over (ĥ)}m is computed and is used for each time sample n in the interval [(m−1)Nd, mNd−1].
In practice, the average error Jhn({right arrow over (ĥ)}) cannot be computed directly, because the joint probability distribution function Phn associated with each impulse response {right arrow over (h)}n is unknown. However, the average error Jhn({right arrow over (ĥ)}) can be approximated by an empirical average error:




  
    
      
        J
        
          h
          n
        
      
      ⁡
      
        (
        
          h
          
            _
            ^
          
        
        )
      
    
    ≈
    
      
        J
        
          (
          m
          )
        
      
      ⁡
      
        (
        
          h
          
            _
            ^
          
        
        )
      
    
  
  =
  
    
      1
      
        
          N
          d
        
        ⁡
        
          (
          
            m
            -
            
              m
              0
            
          
          )
        
      
    
    ⁢
    
      
        ∑
        
          i
          =
          
            
              m
              0
            
            +
            1
          
        
        m
      
      ⁢
      
        
          
          
            
              
                Y
                _
              
              i
            
            -
            
              
                
                  X
                  _
                
                i
              
              ⁢
              
                h
                
                  _
                  ^
                
              
            
          
          
        
        2
      
    
  




where

m0 is any decision epoch,
m>m0, and
the superscript (m) used in this and in subsequent equations identifies the decision epoch.
An approximate impulse response {right arrow over (ĥ)}m can be determined by minimizing the empirical average error J(m)({right arrow over (ĥ)}) over the search space U to give a minimum empirical equation:

{right arrow over (ĥ)}m=( {circumflex over (R)}XX(m)+λmĪ)−1 {circumflex over (R)}XY(m) 

where the overbar identifies a matrix,





  
    
      
        R
        
          _
          ^
        
      
      XX
      
        (
        m
        )
      
    
    =
    
      
        1
        
          
            N
            d
          
          ⁡
          
            (
            
              m
              -
              
                m
                0
              
            
            )
          
        
      
      ⁢
      
        
          ∑
          
            i
            =
            
              
                m
                0
              
              +
              1
            
          
          m
        
        ⁢
        
          
            
              X
              _
            
            i
            T
          
          ⁢
          
            
              X
              _
            
            i
          
        
      
    
  
  ,
  
    

  
  ⁢
  
    
      
        R
        
          _
          ^
        
      
      XY
      
        (
        m
        )
      
    
    =
    
      
        1
        
          
            N
            d
          
          ⁡
          
            (
            
              m
              -
              
                m
                0
              
            
            )
          
        
      
      ⁢
      
        
          ∑
          
            i
            =
            
              
                m
                0
              
              +
              1
            
          
          m
        
        ⁢
        
          
            
              X
              _
            
            i
            T
          
          ⁢
          
            
              Y
              _
            
            i
          
        
      
    
  
  ,




Ī is an m by m identity matrix,



  
    
      
        
          X
          _
        
        i
      
      =
      
        [
        
          
            
              
                x
                ⁡
                
                  [
                  
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        N
                        d
                      
                    
                    -
                    1
                  
                  ]
                
              
            
            
              ⋯
            
            
              
                x
                ⁡
                
                  [
                  
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        N
                        d
                      
                    
                    -
                    L
                  
                  ]
                
              
            
          
          
            
              
                x
                ⁡
                
                  [
                  
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        N
                        d
                      
                    
                    -
                    2
                  
                  ]
                
              
            
            
              ⋯
            
            
              
                x
                ⁡
                
                  [
                  
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        N
                        d
                      
                    
                    -
                    L
                    -
                    1
                  
                  ]
                
              
            
          
          
            
              ⋮
            
            
              ⋱
            
            
              ⋮
            
          
          
            
              
                x
                ⁡
                
                  [
                  
                    
                      (
                      
                        i
                        -
                        1
                      
                      )
                    
                    ⁢
                    
                      N
                      d
                    
                  
                  ]
                
              
            
            
              ⋯
            
            
              
                x
                ⁡
                
                  [
                  
                    
                      
                        (
                        
                          i
                          -
                          1
                        
                        )
                      
                      ⁢
                      
                        N
                        d
                      
                    
                    -
                    L
                    +
                    1
                  
                  ]
                
              
            
          
        
        ]
      
    
    ,
    and
  




  
    
      
        Y
        _
      
      T
    
    =
    
      
        [
        
          
            
              
                x
                ⁡
                
                  [
                  
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        N
                        d
                      
                    
                    -
                    1
                  
                  ]
                
              
            
            
              
                x
                ⁡
                
                  [
                  
                    
                      i
                      ⁢
                      
                        
                      
                      ⁢
                      
                        N
                        d
                      
                    
                    -
                    2
                  
                  ]
                
              
            
            
              ⋯
            
            
              
                x
                ⁡
                
                  [
                  
                    
                      (
                      
                        i
                        -
                        1
                      
                      )
                    
                    ⁢
                    
                      N
                      d
                    
                  
                  ]
                
              
            
          
        
        ]
      
      T
    
  



The constant λm in the minimum empirical equation is a smallest positive value that ensures {right arrow over (ĥ)}m is an element of the search space U. However, using the minimum empirical equation to determine the approximate impulse response {right arrow over (ĥ)}m is computationally demanding. The computational demand can be reduced by applying a stochastic approximation in the form of a recursive equation:

{right arrow over (ĥ)}={right arrow over (ĥ)}m-1+γm Qm[ X′m( Ym− Xm{right arrow over (ĥ)}m-1)]  Equation (2)

where

 Qm is a matrix with elements determined as described below with reference to a control-flow diagram shown in FIG. 14, and
γm is a scalar quantity and is determined as described below with reference to a control-flow diagram shown in FIG. 16.
The methods and systems of the present invention employ the recursive equation to determine the approximate impulse-response vector {right arrow over (ĥ)}m, which also satisfies the following condition:

ĥmεHδm(m) 

where




  
    
      H
      
        δ
        m
      
      
        (
        m
        )
      
    
    =
    
      {
      
        
          
            h
            
              _
              ^
            
          
          m
        
        ∈
        
          
            U
            ⁢
            
              :
            
            ⁢
            
              
            
            ⁢
            
              
                J
                
                  (
                  m
                  )
                
              
              ⁡
              
                (
                
                  h
                  
                    _
                    ^
                  
                
                )
              
            
          
          <
          
            
              v
              
                (
                m
                )
              
            
            +
            
              
                δ
                m
              
              ⁢
              
                
                  σ
                  x
                  2
                
                ⁡
                
                  (
                  m
                  )
                
              
              ⁢
              E
            
          
        
      
      }
    
  




  
    
      
        v
        
          (
          m
          )
        
      
      =
      
        
          inf
          
            
              
                h
                
                  _
                  ^
                
              
              m
            
            ∈
            U
          
        
        ⁢
        
          
            J
            
              (
              m
              )
            
          
          ⁡
          
            (
            
              
                h
                
                  _
                  ^
                
              
              m
            
            )
          
        
      
    
    ,
    and
  



δm is a subjectively small positive real number.
III. Implementation
FIG. 9 illustrates a two-location, audio-conference communication system, as shown in FIG. 1, including an echo-control unit that represents an embodiment of the present invention. The system 900 includes DC offset removal units 902 and 904 and an echo-control unit 906. DC offset is a low-frequency distortion often caused by electrical interference. The electrical interference creates a constant voltage that can cause clicks and pops in the sound output from a loudspeaker. The DC offset removal unit 902 corrects the DC offset in the digital signal xrec[n] produced in the far room 104 as follows:

x[n]=ax[n−1]+0.5(1+a)(xrec[n]−xrec[n−1])

where α is a constant ranging from about 0.9 to about 0.9999. The digital signal x[n] is output from the DC offset removal unit 902 and transmitted to the echo control unit 906. The DC offset removal unit 904 corrects the DC offset in the digital signal ymic[n] produced in the near room 102 as follows:

y[n]=ay[n−1]+0.5(1+a)(ymic[n]−ymic[n−1])

The digital signal y[n] is output from the DC offset removal unit 904 and transmitted to the echo control unit 906. The echo-control unit 906 includes a control 908, an impulse response correction 910, a summing junction 912, and an echo control suppressor 914. The digital signal x[n] is transmitted to both the control 908 and the impulse response correction 910, and the digital signal y[n] is transmitted to both the control 908 and the summing junction 912. The control 908 produces an approximate impulse-response vector that is input to impulse response correction 910 which, in turn, is used to produce an approximate acoustic echo. The approximate acoustic echo is transmitted to the summing junction 912 and subtracted from the digital signal y[n] to produce an output digital signal {circumflex over (r)}[n]. Operation of the control 908, impulse response correction 910, and summing junction 912 is described below with reference to FIGS. 10-16. The output digital signal {circumflex over (r)}[n] is input to the echo control suppressor 914, which corrects for amplification, or gain, in the output digital signal {circumflex over (r)}[n] and outputs a resultant digital signal r[n] that is transmitted to the loudspeaker 116 in the far room 104. Operation of the echo control unit 906 is described below with reference to FIGS. 10A-10B and FIG. 12.

Note that in the above description the echo control unit 906 is used to reduce the acoustic echo transmitted from the near room 102 to the far room 104, in FIG. 9. The echo control unit 906 can be located either inside or outside the near room 102. However, in practice, a second echo control unit (not shown) is needed to reduce an acoustic echo transmitted from the far room 104 to the near room 102.
FIGS. 10A-10B show a control-flow diagram that represents an embodiment of the present invention for reducing acoustic echoes in audio signals that are transmitted from the near room 102 to the far room 104. In step 1001 of FIG. 10A, values for parameters are initialized as displayed below in Tables 1-3. Table 1 displays parameters and example associated values that can be used in the equations described below with reference to FIGS. 10-16:










TABLE 1







Parameter
Value



















L
6000



Nd
288



P
5(Nd)



N
8192



β
0.001



η
0.001



λ
0.001



K1
0.995



K2
0.3



Gmax
1.0



Gmin
0.1










Note that the parameter values displayed in Table 1 are example values that correspond to particular near room and far room conditions and configurations, and are not intended to restrictive. In other applications of the present invention, these parameters can be adjusted in order to accommodate different near room and far room conditions and different configurations of the near room and far room. The parameter P is the number of digital signals y(m)[n] in the digital signal vector {right arrow over (y)}(m)[n] described below with reference to step 1004 in FIG. 10A. The parameter N is the number of digital signals used to form the frequency domain vectors {right arrow over (X)}(m), {right arrow over (y)}(m), and {right arrow over (Ĥ)}(m). The parameters β, η, λ, K1, and K2 are values that are used to assign relative importance or weight to terms in equations described below with reference to FIGS. 10-14. The parameters Gmax and Gmin are the maximum and minimum gain associated with the microphone 106. Table 2 shows initial values for variable parameters that change during iterations of the methods described below with reference to FIGS. 11-12:











TABLE 2







Parameter
Initial Value



















{dot over (σ)}x2(0)
0.01



{dot over (σ)}y2(0)
0.01



{dot over (σ)}{circumflex over (r)}2(0)
0.01



 
0.01



 
0.01



 
0.01



Mx2(0)
0



My2(0)
0



G(0)
0










The parameters {dot over (σ)}x2(0) and {dot over (σ)}y2(0) are short-term energy variances associated with the digital signals x(m)[n] and y(m)[n], respectively. The parameter {dot over (σ)}{circumflex over (r)}2(0) is the short-term energy variance associated with the energy in the output signal {circumflex over (r)}[n]. The parameters x2(0) and y2(0) are long-term energy variances associated with the digital signals x(m)[n] and y(m)[n], respectively. The parameter n2(0) is a long-term energy variance associated with the noise v[n]. The parameters Mx2(0) and My2(0) are maximum square energies associated with the digital signals x(m)[n] and y(m)[n]. The parameter G(0) is an initial gain adaptation value described below with reference to FIG. 12. Table 3 shows initial values for components of vectors {right arrow over (S)}xx(0), {right arrow over (S)}{tilde over (r)}{tilde over (r)}(0), {right arrow over (Λ)}(0), {right arrow over ({tilde over (h)})}(0) and {right arrow over (ĥ)}(0) that change during iterations of the method described below with reference to FIGS. 13-14:












TABLE 3







Vector Component
Initial Value
Component Index









Sxx(0)[k]
1.0
k = 0, . . . , N − 1



S{tilde over (r)}{tilde over (r)}(0)[k]
1.0
k = 0, . . . , N − 1



Λ(0)′[n′]
1.0
n′ = 0, . . . , L − 1



{tilde over (h)}(0)[n′]
0.0
n′ = 0, . . . , L − 1



ĥ(0)[n′]
0.0
n′ = 0, . . . , L − 1










The vector {right arrow over (S)}xx(0) is an initial average spectrum associated with the vector {right arrow over (X)}(m) and the vector {right arrow over (S)}{tilde over (r)}{tilde over (r)}(0) is an initial average spectrum associated with a vector {right arrow over ({tilde over (R)})}(m), which are described below with reference to step 1302 in FIG. 13A. The vector {right arrow over (Λ)}(0) defines an evolving hyper-elliptical region described below with reference to step 1305 in FIG. 13A. The vector {right arrow over ({tilde over (h)})}(0) is an initial shadow-impulse-response vector described below with reference to step 1308 in FIG. 13A. The vector {right arrow over (ĥ)}(0) is an initial impulse-response vector described below with reference to step 1309 in FIG. 13A. In the for-loop beginning in step 1002, steps 1003-1022 are repeated for each decision epoch m. In the for-loop beginning in step 1003, steps 1004-1012 are repeated for each time sample n. In step 1004, a digital signal x(m)[n] is output from the DC offset 902, and a digital signal y(m)[n] is output from the DC offset 904, in FIG. 9. In step 1005, the digital signals x(m)[n] are used to form an (L+P)-component digital signal vector:





  
    
      
        
          x
          _
        
        
          (
          m
          )
        
      
      ⁡
      
        [
        n
        ]
      
    
    =
    
      [
      
        
          
            
              
                x
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                n
                ]
              
            
          
        
        
          
            
              
                x
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                
                  n
                  -
                  1
                
                ]
              
            
          
        
        
          
            ⋮
          
        
        
          
            
              
                x
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                
                  n
                  -
                  
                    (
                    
                      L
                      +
                      P
                      -
                      1
                    
                    )
                  
                
                ]
              
            
          
        
      
      ]
    
  
  ,




and the digital signals y(m)[n] are used to form a P-component digital signal vector:





  
    
      
        y
        _
      
      
        (
        m
        )
      
    
    ⁡
    
      [
      n
      ]
    
  
  =
  
    [
    
      
        
          
            
              y
              
                (
                m
                )
              
            
            ⁡
            
              [
              n
              ]
            
          
        
      
      
        
          
            
              y
              
                (
                m
                )
              
            
            ⁡
            
              [
              
                n
                -
                1
              
              ]
            
          
        
      
      
        
          ⋮
        
      
      
        
          
            
              y
              
                (
                m
                )
              
            
            ⁡
            
              [
              
                n
                -
                
                  (
                  
                    P
                    -
                    1
                  
                  )
                
              
              ]
            
          
        
      
    
    ]
  




In step 1006, a FFT is applied to the vectors {right arrow over (x)}(m)[n], {right arrow over (y)}(m)[n] and {right arrow over (ĥ)}(m−1) in order to obtain frequency domain vectors:




  
    
      
        
          X
          _
        
        
          (
          m
          )
        
      
      =
      
        
          [
          
            
              
                
                  
                    X
                    
                      (
                      m
                      )
                    
                  
                  ⁡
                  
                    [
                    0
                    ]
                  
                
              
            
            
              
                
                  
                    X
                    
                      (
                      m
                      )
                    
                  
                  ⁡
                  
                    [
                    1
                    ]
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    X
                    
                      (
                      m
                      )
                    
                  
                  ⁡
                  
                    [
                    
                      N
                      -
                      1
                    
                    ]
                  
                
              
            
          
          ]
        
        =
        
          FFT
          ⁢
          
            {
            
              [
              
                
                  
                    
                      
                        x
                        
                          (
                          m
                          )
                        
                      
                      ⁡
                      
                        [
                        n
                        ]
                      
                    
                  
                
                
                  
                    
                      
                        x
                        
                          (
                          m
                          )
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          -
                          1
                        
                        ]
                      
                    
                  
                
                
                  
                    ⋮
                  
                
                
                  
                    
                      
                        x
                        
                          (
                          m
                          )
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          -
                          
                            (
                            
                              L
                              +
                              P
                              -
                              1
                            
                            )
                          
                        
                        ]
                      
                    
                  
                
              
              ]
            
            }
          
        
      
    
    ,
    
      

    
    ⁢
    
      
        
          Y
          _
        
        
          (
          m
          )
        
      
      =
      
        
          [
          
            
              
                
                  
                    Y
                    
                      (
                      m
                      )
                    
                  
                  ⁡
                  
                    [
                    0
                    ]
                  
                
              
            
            
              
                
                  
                    Y
                    
                      (
                      m
                      )
                    
                  
                  ⁡
                  
                    [
                    1
                    ]
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    Y
                    
                      (
                      m
                      )
                    
                  
                  ⁡
                  
                    [
                    
                      N
                      -
                      1
                    
                    ]
                  
                
              
            
          
          ]
        
        =
        
          FFT
          ⁢
          
            {
            
              [
              
                
                  
                    
                      
                        y
                        
                          (
                          m
                          )
                        
                      
                      ⁡
                      
                        [
                        n
                        ]
                      
                    
                  
                
                
                  
                    
                      
                        y
                        
                          (
                          m
                          )
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          -
                          1
                        
                        ]
                      
                    
                  
                
                
                  
                    ⋮
                  
                
                
                  
                    
                      
                        y
                        
                          (
                          m
                          )
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          -
                          
                            (
                            
                              P
                              -
                              1
                            
                            )
                          
                        
                        ]
                      
                    
                  
                
              
              ]
            
            }
          
        
      
    
    ,
    and
  




  
    
      
        H
        _
      
      
        (
        
          m
          -
          1
        
        )
      
    
    =
    
      
        [
        
          
            
              
                
                  H
                  
                    (
                    
                      m
                      -
                      1
                    
                    )
                  
                
                ⁡
                
                  [
                  0
                  ]
                
              
            
          
          
            
              
                
                  H
                  
                    (
                    
                      m
                      -
                      1
                    
                    )
                  
                
                ⁡
                
                  [
                  1
                  ]
                
              
            
          
          
            
              ⋮
            
          
          
            
              
                
                  H
                  
                    (
                    
                      m
                      -
                      1
                    
                    )
                  
                
                ⁡
                
                  [
                  
                    N
                    -
                    1
                  
                  ]
                
              
            
          
        
        ]
      
      =
      
        FFT
        ⁢
        
          {
          
            [
            
              
                
                  
                    
                      h
                      
                        (
                        
                          m
                          -
                          1
                        
                        )
                      
                    
                    ⁡
                    
                      [
                      n
                      ]
                    
                  
                
              
              
                
                  
                    
                      h
                      
                        (
                        
                          m
                          -
                          1
                        
                        )
                      
                    
                    ⁡
                    
                      [
                      
                        n
                        -
                        1
                      
                      ]
                    
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    
                      h
                      
                        (
                        
                          m
                          -
                          1
                        
                        )
                      
                    
                    ⁡
                    
                      [
                      
                        n
                        -
                        
                          (
                          
                            L
                            -
                            1
                          
                          )
                        
                      
                      ]
                    
                  
                
              
            
            ]
          
          }
        
      
    
  



In step 1007, an output signal vector is computed as follows:

{right arrow over ({circumflex over (r)})}(m)[n]=TrNd·IFFT{{right arrow over (Y)}(m)−{right arrow over (X)}(m)∘({right arrow over (Ĥ)}(m−1))*}

where

TrNd is a truncation operator of length Nd,
“∘” represents component-wise multiplication of two vectors,




  
    
      
        
          
            r
            _
          
          ^
        
        
          (
          m
          )
        
      
      ⁡
      
        [
        n
        ]
      
    
    =
    
      [
      
        
          
            
              
                
                  r
                  ^
                
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                n
                ]
              
            
          
        
        
          
            
              
                
                  r
                  ^
                
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                
                  n
                  -
                  1
                
                ]
              
            
          
        
        
          
            ⋮
          
        
        
          
            
              
                
                  r
                  ^
                
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                
                  n
                  -
                  
                    (
                    
                      
                        N
                        d
                      
                      -
                      1
                    
                    )
                  
                
                ]
              
            
          
        
      
      ]
    
  
  ,
  and




{circumflex over (r)}(m)[n] is the output digital signal output from the summing junction 912, in FIG. 9.
Component-wise multiplication of the 3-tuples (1,2,3) and (3,1,2) is represented by:

(1,2,3){circle around (×)}(3,1,2)=(1·3,2·1,3·2)=(3,2,6)

In step 1008, the routine “determine control state” is called, which identifies four types of audio transmissions that can exist between the near room 102 and the far room 104, in FIG. 9. The four kinds of audio transmission are called “control states” (“CS”) and are identified as follows: (1) an audio signal is output from the near end room 102 only and is represented by SNEO; (2) an audio signal is output from the far end room 104 only and is represented by SFEO; (3) audio signals are simultaneously output from both the near end room 102 and the far end room 104, which is called “double-talk,” is represented by SDT; and (4) no audio signals output from the near end room 102 and the far end room 104 is represented by SNS. In step 1009, the routine “residual echo suppression” is called in order to compute a gain-corrected output digital signal r(m)[n], as described above with reference to echo suppression 914, in FIG. 9. In step 1010, the gain-corrected output digital signal r(m)[n] is transmitted to loudspeaker 116, in FIG. 9.

In step 1011 of FIG. 10B, when n is less than mNd−1, control passes to step 1012, otherwise control passes to step 1013. In step 1012, the time sample n is incremented by “1,” and steps 1004-1011 are repeated. In step 1013, when another decision epoch m is available, control passes to step 1014, otherwise the routine “determine r[n]” is terminated. In step 1014, the decision epoch m is incremented by “1.” In step 1015, when the CS is SNEO or SNS, control passes to step 1016, otherwise control passes to step 1017. In step 1016, the impulse-response vector is updated by assigning elements in the vector {right arrow over (ĥ)}(m) to corresponding values in the impulse response {right arrow over (ĥ)}(m−1) from the previous decision period, and the shadow-impulse-response vector is updated by assigning elements in the shadow-impulse-response vector {right arrow over ({tilde over (h)})}(m) to corresponding elements in the shadow-impulse-response vector {right arrow over ({tilde over (h)})}(m−1) from the previous decision period. In step 1017, when the CS is SFEO, control passes to step 1018, otherwise the CS is SDT and control passes to step 1019. In step 1018, the routine “determine {right arrow over (ĥ)}(m)” is called and an approximate impulse-response vector {right arrow over (ĥ)}(m) is computed. In step 1019, when “count” does not equal “0,” control passes to step 1020, otherwise control passes to step 1021. In step 1020, the “count” is decremented by “1” and control passes to step 1016. In step 1021, the approximate impulse-response vector {right arrow over (ĥ)}(m) is selected form an impulse-response data structure represented by the set {{right arrow over (ĥ)}(mK), . . . , {right arrow over (ĥ)}(m1)}. This data structure includes the K most recent approximate impulse responses with the highest signal to noise ratio. Note that the approximate impulse-response vector is not updated during double talk because during double talk the signal-to-noise ratio decreases rapidly. The increased noise distorts the approximate impulse-response vector. In order to avoid this distortion, the approximate impulse-response vector is selected from the impulse-response data structure. The subscripts on the decision epochs m correspond to the order in which the impulse response vectors have been added to the data structure. For example, the impulse response vector {right arrow over (ĥ)}(mK) has been in the data structure the longest, and the impulse response vector {right arrow over (ĥ)}(m1) is the most recent addition to the data structure.
In various embodiments of the present invention, the approximate impulse-response vector can be selected based on any number of different criteria. For example, in one embodiment of the present invention, an approximate impulse-response vector can be selected in step 1021 according to which impulse-response vector has the largest corresponding ERLE(mi). In another embodiment of the present invention, in step 1021, the approximate impulse-response vector that has been in the data structure the longest is selected, which is {right arrow over (ĥ)}(mK). The impulse-response data structure is updated in the routine “determine {right arrow over (ĥ)}(m),” which is described below with reference to steps 1310 and 1312, in FIG. 13A. The associated value of ERLE(m) is computed in the routine “determine control state.” In step 1022, “count” is assigned a value “M.” The value M can be 10, 12, 15, 18, or any other suitable value.
FIGS. 10C-10D shows two plots of amplification energy versus time for the four types of control states that represents an embodiment of the present invention. In FIGS. 10C-10D, vertical axes, such as vertical axis 1030, represent amplification energy associated with signals transmitted between the near room 102 and the far room 104, horizontal axes, such as horizontal axis 1032, represent time, and horizontal dashed lines, such as dashed line 1034, correspond to a double talk threshold energy. Curves 1036 and 1038 represent the amplification energies associated with signals transmitted between the near room 102 and the far room 104. Amplification energies below the double talk threshold 1034 are associated with an SFEO, SNEO, or SNS control state. Peak 1040 corresponds to amplification energy resulting from double talk, which exceeds the double talk threshold 1034. However, peak 1042 corresponds to a noise produced in the near room 102 or the far room 104. This noise initially creates the appearance of double talk because the amplification energy exceeds the double talk threshold energy 1034, even though double talk is not actually taking place. In order to avoid short duration noises from being misinterpreted as double talk, at time 1044, a countdown begins with the variable “count,” described in step 1019, set equal to M. This countdown takes place in steps 1019 and 1020, which avoids selecting an approximate impulse-response vector from the data structure {{right arrow over (ĥ)}(mK), . . . , {right arrow over (ĥ)}(m1)} in step 1021 until double talk can be confirmed for M iterations. In other words, the method of the present invention continues operating as if double talk has not occurred for M decision periods. If after M iterations the amplification energy has decreased, as indicated at time 1046 in FIG. 10C, inappropriate selection of an approximate impulse-response vector for double talk has been avoided. On the other hand, if after M iterations the amplification energy has increased, as indicated by time 1048 in FIG. 10D, an approximate impulse-response for double talk is selected in step 1021.
FIGS. 11A-11C show a control-flow diagram for the routine “determine control state” called in step 1008 in FIG. 10A and represents an embodiment of the present invention. In FIG. 11A, step 1101, average square energies associated with the vectors {right arrow over (x)}(m)[n], {right arrow over (y)}(m)[n], {right arrow over ({circumflex over (r)})}(m)[n], and a shadow-error vector {right arrow over ({tilde over (r)})}(m)[n] are:

Ex2(m)=∥{right arrow over (x)}(m)[n]∥2,

Ey2(m)=∥{right arrow over (y)}(m)[n]∥2,

E{circumflex over (r)}2(m)=∥{right arrow over ({circumflex over (r)})}(m)[n]∥2,

and

E{right arrow over (r)}2(m)=∥{right arrow over ({tilde over (r)})}(m)[n]∥2 

In step 1102, long-term energy variances are recursively determined for the average square energies by:

x2(m)[n]=0.99x2(m−1)[n]+0.01Ex2(m),

y2(m)[n]=0.99y2(m−1)[n]+0.01Ey2(m),

and

n2(m)[n]=0.99n2(m−1)[n]+0.01E{tilde over (r)}2(m),

The coefficients 0.99 and 0.01 are weights that assign a higher relative importance to the variances x2(m−1)[n], y2(m−1)[n], and n2(m−1)[n] than to the average square energies Ex2(m), Ey2(m), and E{tilde over (r)}2(m). In steps 1103-1107, a maximum square energy Mx2(m) associated with the digital signal vector {right arrow over (x)}(m)[n] is determined. In step 1103, when the maximum square energy Mx2(m−1) is less than the average square energy Ex2(m) control passes to step 1104, otherwise control passes to step 1105. In step 1104, the maximum square energy is computed by:

Mx2(m)=min{Ex2(m),10Mx2(m−1)}

and control passes to step 1108. In step 1105, when the average square energy Ex2(m) is greater than the maximum square energy Mx2(m−1) control passes to step 1106, otherwise control passes to step 1107. In step 1106, the maximum square energy is computed by:

Mx2(m)=0.999Mx2(m−1)+0.001Ex2(m) 

and control passes to step 1108. The coefficients 0.999 and 0.001 assign a higher relative importance to the maximum square energy Mx2(m−1) than to the average square energy Ex2(m). In step 1107, the maximum square energy Mx2(m) is assigned the value of Mx2(m−1). In steps 1108-1112, a maximum square energy My2(m) associated with the digital signal vector {right arrow over (y)}(m)[n] is determined. In step 1108, when the maximum square energy My2(m−1) is less than the average square energy Ey2(m) control passes to step 1109, otherwise control passes to step 1110. In step 1109, the maximum square energy is computed by:

My2(m)=min{Ey2(m),10My2(m−1)}

and control passes to step 1113, in FIG. 11B. In step 1110, when the average square energy Ey2(m) is greater than the maximum square energy My2(m−1) control passes to step 1111, otherwise control passes to step 1112. In step 1111, the maximum square energy is computed by:

My2(m)=0.999My2(m−1)+0.001Ey2(m) 

and control passes to step 1113. In step 1112, the maximum energy My2(m) is assigned the value of My2(m−1).

In steps 1113-1124 of FIG. 11B, the average square energies Ex2(m) and E{tilde over (r)}2(m), long-term energy variances x2(m)[n], y2(m)[n], and n2(m)[n], and maximum energies Mx2(m) and My2(m) are used to determine logic “TRUE” or “FALSE” values of Boolean variables T1, T2, T3, and T4, which are subsequently used in the control-flow diagram in FIG. 11C to determine the CS. In step 1113, when the average square energy E{tilde over (r)}2(m) is greater than or equal to 0.05y2(m−1)[n]/n2(m−1)[n], control passes to step 1114 and T1 is set to “TRUE,” otherwise control passes to step 1115 and T1 is set to “FALSE.” In step 1116, when the average square energy Ex2(m) is greater than or equal to 0.01Mx2(m), control passes to step 1117 and T2 is set to “TRUE,” otherwise control passes to step 1118 and T2 is set to “FALSE.” In step 1119, when the long-term variance x2(m)[n] is less than 0.01Mx2(m), control passes to step 1120 and T3 is set to “TRUE,” otherwise control passes to step 1121 and T3 is set to “FALSE.” In step 1122, when the long-term variance y2(m)[n] is less than 0.01My2(m), control passes to step 1123 and T4 is set to “TRUE,” otherwise control passes to step 1124 and T4 is set to “FALSE.”
In steps 1125-1131 of FIG. 11C, the Boolean logic values determined in steps 1113-1124 are used to determine the CS. In step 1125, when T1 and T3 are “TRUE,” and T2 and T4 are “FALSE,” control passes to step 1126 and CS is SNEO, otherwise control passes to step 1127. In step 1127, when T3 and T4 are “TRUE,” and T2 is “FALSE,” control passes to step 1128, and CS is SNS, otherwise control passes to step 1129. In step 1129, when T2 is “TRUE” and T1, T3, and T4 are “FALSE,” control passes to step 1130, and CS is SFEO, otherwise control passes to step 1131. In step 1131, when T1 and T2 are “TRUE,” and T3 and T4 are “FALSE,” control passes to step 1132, and CS is SDT, otherwise control passes to step 1133. In step 1133, short-term variances associated with the average square energies Ex2(m) and E{tilde over (r)}2(m) are given by:

{dot over (σ)}y2(m)[n]=0.8{dot over (σ)}y2(m−1)[n]+0.2Ey2(m),

and

{dot over (σ)}{circumflex over (r)}2(m)[n]=0.8{dot over (σ)}{circumflex over (r)}2(m−1)[n]+0.2E{circumflex over (r)}2(m) 

The short-term variance coefficients 0.8 and 0.2 are weights that assign a higher relative importance to the variances {dot over (σ)}y2(m−1)[n] and {dot over (σ)}{circumflex over (r)}2(m−1)[n] than to the average square energies Ey2(m) and E{right arrow over (r)}2(m). In step 1134, the short-term variances determined in step 1132 are used to calculate an echo return loss enhancement value (“ERLE”) given by:





  
    ERLE
    
      (
      m
      )
    
  
  =
  
    10
    ⁢
    
      
    
    ⁢
    
      
        log
        10
      
      ⁡
      
        (
        
          
            
              
                σ
                .
              
              y
              
                2
                ⁢
                
                  (
                  m
                  )
                
              
            
            ⁡
            
              [
              n
              ]
            
          
          
            
              
                σ
                .
              
              
                r
                ^
              
              
                2
                ⁢
                
                  (
                  m
                  )
                
              
            
            ⁡
            
              [
              n
              ]
            
          
        
        )
      
    
  




The ERLE can be used to gauge the performance of acoustic echo cancellation when the system is in the state SFEO. The value of ERLE(m) is larger during SFEO than during SDT.

FIG. 12 is a control-flow diagram for the routine “residual echo suppression” called in step 1009 in FIG. 10A and represents an embodiment of the present invention. The CS of the audio transmission can be used to correct for gain in the output digital signal {circumflex over (r)}[n]. For example, during double-talk, or when an audio signal is produced in the near end room only, the gain acquired by the output digital signal {circumflex over (r)}[n] is larger than when an audio signal is produced in the far end room only or when there is no audio signal. The maximum and minimum amounts of gain that the output digital signal can acquire are represented by the constants Gmax and Gmin, respectively. Steps 1201-1204 adjust the gain in output digital signal {circumflex over (r)}[n] in accordance with the current CS. In step 1201, when the CS is SDT or SNEO, control passes to step 1202, otherwise the CS is either SNS or SNEO and control passes to step 1203. In step 1202, the gain is computed as follows:

G(m)=K2G(m−1)+(1−K2)Gmax 

where K2 is a weight assigning a lower relative importance to G(m−1) than to the maximum gain Gmax. In step 1203, the gain is computed as follows:

G(m)=K1G(m−1)+(1−K1)Gmin 

where K1 is a weight assigning a higher relative importance to G(m−1) than to the minimum gain Gmin. In step 1204, the residual signal is determined by:

r(m)[n]=G(m){circumflex over (r)}(m)[n]

FIG. 13A is a control-flow diagram for the routine “determine {right arrow over (ĥ)}(m)” called in step 1018 in FIG. 10A and represents an embodiment of the present invention. In step 1301, the FFT is applied to the vector {right arrow over ({tilde over (h)})}(m−1) in order to obtain a frequency domain dependent vector:




  
    
      
        
          
            H
            
              _
              ~
            
          
          
            (
            
              m
              -
              1
            
            )
          
        
        =
        
        ⁢
        
          [
          
            
              
                
                  
                    
                      H
                      ~
                    
                    
                      (
                      
                        m
                        -
                        1
                      
                      )
                    
                  
                  ⁡
                  
                    [
                    0
                    ]
                  
                
              
            
            
              
                
                  
                    
                      H
                      ~
                    
                    
                      (
                      
                        m
                        -
                        1
                      
                      )
                    
                  
                  ⁡
                  
                    [
                    1
                    ]
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    
                      H
                      ~
                    
                    
                      (
                      
                        m
                        -
                        1
                      
                      )
                    
                  
                  ⁡
                  
                    [
                    
                      N
                      -
                      1
                    
                    ]
                  
                
              
            
          
          ]
        
      
    
  
  
    
      
        =
        
        ⁢
        
          FFT
          ⁢
          
            {
            
              [
              
                
                  
                    
                      
                        
                          h
                          
                            _
                            ~
                          
                        
                        
                          (
                          
                            m
                            -
                            1
                          
                          )
                        
                      
                      ⁡
                      
                        [
                        n
                        ]
                      
                    
                  
                
                
                  
                    
                      
                        
                          h
                          
                            _
                            ~
                          
                        
                        
                          (
                          
                            m
                            -
                            1
                          
                          )
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          -
                          1
                        
                        ]
                      
                    
                  
                
                
                  
                    ⋮
                  
                
                
                  
                    
                      
                        
                          h
                          
                            _
                            ~
                          
                        
                        
                          (
                          
                            m
                            -
                            1
                          
                          )
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          -
                          
                            (
                            
                              L
                              -
                              1
                            
                            )
                          
                        
                        ]
                      
                    
                  
                
              
              ]
            
            }
          
        
      
    
  




In step 1302, a frequency domain, shadow-error vector is computed as follows:





  
    
      R
      
        _
        ~
      
    
    
      (
      m
      )
    
  
  =
  
    
      FFT
      ·
      
        Tr
        P
      
      ·
      IFFT
    
    ⁢
    
      {
      
        
          
            Y
            _
          
          
            (
            m
            )
          
        
        -
        
          
            
              X
              _
            
            
              (
              m
              )
            
          
          ·
          
            
              (
              
                
                  H
                  
                    _
                    ~
                  
                
                
                  (
                  
                    m
                    -
                    1
                  
                  )
                
              
              )
            
            *
          
        
      
      }
    
  




where

TrP is a truncation operator of length P, and




  
    
      R
      
        _
        ~
      
    
    
      (
      m
      )
    
  
  =
  
    [
    
      
        
          
            
              
                R
                ~
              
              
                (
                m
                )
              
            
            ⁡
            
              [
              0
              ]
            
          
        
      
      
        
          
            
              
                R
                ~
              
              
                (
                m
                )
              
            
            ⁡
            
              [
              1
              ]
            
          
        
      
      
        
          ⋮
        
      
      
        
          
            
              
                R
                ~
              
              
                (
                m
                )
              
            
            ⁡
            
              [
              
                N
                -
                1
              
              ]
            
          
        
      
    
    ]
  




In step 1303, an IFFT is applied to the frequency domain, shadow-error vector in order to obtain a shadow-error vector:

{right arrow over ({tilde over (r)})}(m)=FFT{{right arrow over ({tilde over (R)})}(m)}

In step 1304, the routine “determine {right arrow over ({tilde over (ε)})}(m)” is called. In step 1305, an evolving hyper-ellipsoid-specification vector is determined in accordance with the following recursive formula:

{right arrow over (Λ)}(m)=(1−η){right arrow over (Λ)}(m−1)+η{right arrow over (ĥ)}(m−1)∘{right arrow over (ĥ)}(m−1) 

The parameter η is a weight that assigns greater importance to {right arrow over (Λ)}(m−1) than to {right arrow over (ĥ)}(m−1)∘{right arrow over (ĥ)}(m−1). The hyper-ellipsoid-specification vector {right arrow over (Λ)}(m) is used to compute the shadow update step size μm in the routine “determine μm” called in step 1306. The hyper-ellipsoid-specification vector {right arrow over (Λ)}(m) is also used to compute and the adaptation step size γm in the routine “determine γm” called in step 1307. In step 1308, the shadow mismatch vector {right arrow over ({tilde over (ε)})}(m), determined in step 1304, and the shadow update step size μm, determined in step 1306, are used to recursively compute a shadow-impulse-response vector:

{right arrow over ({tilde over (h)})}(m)={right arrow over ({tilde over (h)})}(m−1)+μm{right arrow over ({tilde over (ε)})}(m) 

In step 1309, the adaptation step size γm, determined in step 1307, is used to recursively compute the approximate impulse-response vector as follows:

{right arrow over (ĥ)}(m)=(1−γm){right arrow over (ĥ)}(m−1)+γm{right arrow over ({tilde over (h)})}(m) 

The parameter γm is used to weight the level of importance to the shadow-impulse-response vector {right arrow over ({tilde over (h)})}(m). In step 1310, when the ERLE ERLE(m) is greater than a threshold value C, control passes to step 1311. The threshold value C can be 10, 12, 15, or any other suitable value for weighting the approximate impulse-response vector {right arrow over (ĥ)}(m). In step 1311, the impulse-response data structure described above with reference to step 1021:

{{right arrow over (ĥ)}(mK),{right arrow over (ĥ)}(mK-1), . . . , {right arrow over (ĥ)}(m2),{right arrow over (ĥ)}(m1)}

is updated.

The impulse-response vectors are arranged in the impulse-response data structure in order of increasing decision epoch values as follows mK<mK−1< . . . <m2<m1, where the decision epoch mK corresponds to an approximate impulse-response vector that has been in the data structure for the longest period of time, and the decision epoch m1 corresponds to the most recent approximate impulse-response vector added to the data structure. In one embodiment of the present invention, the data structure can be updated in step 1311 by removing the impulse-response vector {right arrow over ({tilde over (h)})}(mK) from the data structure and adding the most recently computed impulse-response vector {right arrow over ({tilde over (h)})}(m) to the data structure computed in step 1309, which gives the impulse response data structure:

{{right arrow over (ĥ)}(mK-1), . . . , {right arrow over (ĥ)}(m2),{right arrow over (ĥ)}(m1),{right arrow over (ĥ)}(m)}

In other embodiments of the present invention, the data structure can be updated in step 1311 according to the magnitude of the ERLE values associated with each approximate impulse-response vector. For example, the approximate impulse-response vector with the smallest associated ERLE value is removed from the data structure in order to accommodate addition of the most recently computed approximate impulse-response vector computed in step 1309 and satisfying the threshold condition in steps 1310.

The shadow update step size μm determined by the routine called in the step 1306 substantially ensures that the shadow-impulse-response vector {right arrow over ({tilde over (h)})}(m) determined in the step 1308 lies within an evolving “trust region” that lies within the search space U. This trust region can be a hype-spherical region, a hyper-elliptical region, a hyper-cubic region, or any other hyper-dimension region that lies within the search space.
In one embodiment of the present invention described with reference to FIG. 13B, the trust region is assumed to be a hyper-elliptical region that lies within the search space. FIG. 13B provides a two-dimensional illustration of a hyper-elliptical region located within the search space U 1322 that represents an embodiment of the present invention. Although in FIG. 13B the regions 1320 and 1322 are represented in two-dimensions, in practice these regions are actually L-dimensional vector subspaces of L and are centered at the origin of L. The shape of the hyper-elliptical region 1320 is determined by the hyper-ellipsoid-specification vector {right arrow over (Λ)}(m-1) computed in step 1305. In other words, as shown in FIG. 13B, six previously determined shadow-impulse-response vectors represented by dots lie within the hyper-elliptical region 1320 which is associated with the hyper-ellipsoid-specification vector {right arrow over (Λ)}(m-1). The hyper-elliptical region 1320 is referred to as an “evolving” hyper-elliptical region because when a subsequent hyper-ellipsoid-specification vector {right arrow over (Λ)}(m) is determined, the associated region changes orientation within the search space U 1322 but this newly oriented elliptical region retains a substantially elliptical shape. A newly computed shadow-impulse-response vector {right arrow over ({tilde over (h)})}(m) computed according to the recursive formula:

{right arrow over ({tilde over (h)})}(m)={right arrow over ({tilde over (h)})}(m-1)+μm{right arrow over ({tilde over (ε)})}(m) 

falls within a newly oriented hyper-elliptical region because the shadow update step size μm is a function of the hyper-ellipsoid-specification vector {right arrow over (Λ)}(m), as described below with reference to FIG. 15. As shown in FIG. 13B, when the magnitude and direction of the shadow mismatch vector {right arrow over ({tilde over (ε)})}(m) is large, as indicated by vector 1324, the shadow update step size μm reduces the magnitude and changes the direction of the shadow mismatch vector {right arrow over ({tilde over (ε)})}(m), as indicated by vector 1326, so that the shadow-impulse-response vector {right arrow over ({tilde over (h)})}(m) lies within a newly oriented hyper-elliptical region 1328.

Note that in other embodiments of the present invention, rather than computing a single shadow update step size μm to update the shadow impulse-response vector, the magnitude of the shadow impulse-response vector can be changed so that it lies within the trust region by computing a vector that is added to the shadow impulse-response vector in order to adjust the individual components of the shadow impulse-response vector.
FIG. 14 is a control-flow diagram for the routine “determine {right arrow over ({tilde over (ε)})}(m)” called in step 1304 in FIG. 13 and represents an embodiment of the present invention. In step 1401, an average spectrum of the frequency domain vector {right arrow over (X)}(m) is computed as follows:

{right arrow over (S)}xx(m)=(1−β){right arrow over (S)}xx(m−1)+β{right arrow over (X)}(m)∘{right arrow over (X)}(m) 

and an average spectrum of the vector {right arrow over ({tilde over (R)})}(m) is computed as follows:

{right arrow over (S)}{tilde over (r)}{tilde over (r)}(m)=(1−β){right arrow over (S)}{tilde over (r)}{tilde over (r)}(m−1)+β{right arrow over ({tilde over (R)})}(m)∘{right arrow over ({tilde over (R)})}(m) 

where




  
    
      
        
          S
          _
        
        xx
        
          
            (
            m
            )
          
          ⁢
          
            
          
        
      
      =
      
        [
        
          
            
              
                
                  S
                  xx
                  
                    (
                    m
                    )
                  
                
                ⁡
                
                  [
                  0
                  ]
                
              
            
          
          
            
              
                
                  S
                  xx
                  
                    (
                    m
                    )
                  
                
                ⁡
                
                  [
                  1
                  ]
                
              
            
          
          
            
              ⋮
            
          
          
            
              
                
                  S
                  xx
                  
                    (
                    m
                    )
                  
                
                ⁡
                
                  [
                  
                    N
                    -
                    1
                  
                  ]
                
              
            
          
        
        ]
      
    
    ,
    and
  




  
    
      
        S
        _
      
      rr
      
        (
        m
        )
      
    
    =
    
      [
      
        
          
            
              
                S
                rr
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                0
                ]
              
            
          
        
        
          
            
              
                S
                rr
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                1
                ]
              
            
          
        
        
          
            ⋮
          
        
        
          
            
              
                S
                rr
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                
                  N
                  -
                  1
                
                ]
              
            
          
        
      
      ]
    
  



The parameter β is a weight that assigns greater importance to the vectors {right arrow over (S)}xx(m−1) and {right arrow over (S)}{tilde over (r)}{tilde over (r)}(m−1) than to the products {right arrow over (X)}(m)∘{right arrow over (X)}(m) and {right arrow over ({tilde over (R)})}(m)∘{right arrow over ({tilde over (R)})}(m). In step 1402, the energies computed in FIG. 11 are used to determine:





  
    α
    m
  
  =
  
    5
    ⁢
    
      
        (
        
          
            E
            
              r
              ~
            
            
              2
              ⁢
              
                (
                m
                )
              
            
          
          
            E
            
              r
              ^
            
            
              2
              ⁢
              
                (
                m
                )
              
            
          
        
        )
      
      4
    
    ⁢
    
      
        
          σ
          .
        
        x
        
          2
          ⁢
          
            (
            m
            )
          
        
      
      
        M
        x
        
          2
          ⁢
          
            (
            m
            )
          
        
      
    
  




In steps 1403-1406, elements of an N-component, frequency domain, preconditioning vector {right arrow over (Q)}(m) are determined. In the for-loop beginning in step 1403, steps 1404-1406 are repeated for each frequency domain index k. In step 1404, the elements of the preconditioning vector {right arrow over (Q)}(m) are calculated as follows:





  
    
      Q
      
        (
        m
        )
      
    
    ⁡
    
      [
      k
      ]
    
  
  =
  
    1
    
      max
      ⁢
      
        {
        
          
            
              
                S
                xx
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                k
                ]
              
            
            +
            
              
                α
                m
              
              ⁢
              
                
                  S
                  
                    
                      r
                      ~
                    
                    ⁢
                    
                      r
                      ~
                    
                  
                  
                    (
                    m
                    )
                  
                
                ⁡
                
                  [
                  k
                  ]
                
              
            
          
          ,
          λ
        
        }
      
    
  




where k ranges from 0 to N−1. In step 1405, when k is less than N−1, control passes to step 1406, otherwise control passes to step 1407. In step 1406, the index k is incremented by the value “1.” In step 1407, the vector {right arrow over ({tilde over (ε)})}(m) is computed as follows:





  
    
      
        ɛ
        _
      
      ~
    
    
      (
      m
      )
    
  
  =
  
    
      
        Tr
        L
      
      ·
      IFFT
    
    ⁢
    
      {
      
        
          
            Q
            _
          
          
            (
            m
            )
          
        
        ·
        
          
            X
            _
          
          
            (
            m
            )
          
        
        ·
        
          
            (
            
              
                
                  R
                  _
                
                ~
              
              
                (
                m
                )
              
            
            )
          
          *
        
      
      }
    
  




where

TrL is a truncation operator of size L, and




  
    
      
        ɛ
        _
      
      ~
    
    
      (
      m
      )
    
  
  =
  
    [
    
      
        
          
            
              ɛ
              ~
            
            ⁡
            
              [
              0
              ]
            
          
        
      
      
        
          
            
              ɛ
              ~
            
            ⁡
            
              [
              1
              ]
            
          
        
      
      
        
          ⋮
        
      
      
        
          
            
              ɛ
              ~
            
            ⁡
            
              [
              
                L
                -
                1
              
              ]
            
          
        
      
    
    ]
  




FIG. 15 is a control-flow diagram for the routine “determine μm” called in step 1306 in FIG. 13 that represents an embodiment of the present invention. In step 1501, a parameter μ_scale(m) is computed as follows:




  
    μ_scale
    
      (
      m
      )
    
  
  =
  
    
      ∑
      
        n
        =
        0
      
      
        L
        -
        1
      
    
    ⁢
    
      
        
          (
          
            
              
                ɛ
                ~
              
              
                (
                m
                )
              
            
            ⁡
            
              [
              n
              ]
            
          
          )
        
        2
      
      
        
          Λ
          
            (
            m
            )
          
        
        ⁡
        
          [
          n
          ]
        
      
    
  




In step 1502, when μ_scale(m) is greater than the value “1,” control passes to step 1503, otherwise control passes to step 1504. In step 1503, μm is assigned the value 0.2/√{square root over (μ_scale(m))}. In step 1504, μm is assigned the value “0.2.”

FIG. 16 is a control-flow diagram for the routine “determine γm” called in step 1307 in FIG. 13 that represents an embodiment of the present invention. In step 1601, a parameter γ_scale(m) is computed as follows:




  
    γ_scale
    
      (
      m
      )
    
  
  =
  
    
      1
      L
    
    ⁢
    
      
        ∑
        
          n
          =
          0
        
        
          L
          -
          1
        
      
      ⁢
      
        
          
            (
            
              
                
                  h
                  ~
                
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                n
                ]
              
            
            )
          
          2
        
        
          
            Λ
            
              (
              m
              )
            
          
          ⁡
          
            [
            n
            ]
          
        
      
    
  




In step 1602, when E{tilde over (r)}2≦0.9E{circumflex over (r)}2 for M decision periods, control passes to step 1603, otherwise, control passes to step 1604. In step 1603, a parameter cm is computed recursively as follows:

cm=max{cm-1−4000,400}

In step 1604, the parameter cm is computed recursively as follows:

cm=max{cm-1+1,40000}

In step 1605, γm is assigned a value according to:





  
    γ
    m
  
  =
  
    5
    ⁢
    
      
        (
        
          
            α
            m
          
          
            
              α
              m
            
            +
            
              c
              m
            
          
        
        )
      
      .85
    
  




where αm is computed in step 1402 of FIG. 14. In step 1606, when γ_scale(m) is greater than “1,” control passes to step 1607. In step 1607, γm is assigned the value:





  
    γ
    m
  
  =
  
    
      γ
      m
    
    
      
        γ_scale
        
          (
          m
          )
        
      
    
  




The foregoing description, for purposes of explanation, used specific nomenclature to provide a thorough understanding of the invention. However, it will be apparent to one skilled in the art that the specific details are not required in order to practice the invention. The foregoing descriptions of specific embodiments of the present invention are presented for purposes of illustration and description. They are not intended to be exhaustive of or to limit the invention to the precise forms disclosed. Obviously, many modifications and variations are possible in view of the above teachings. The embodiments are shown and described in order to best explain the principles of the invention and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims and their equivalents:

## Claims

1. A method for determining an approximate impulse-response vector for canceling an acoustic echo resulting from an audio signal transmitted from a first location to a second location using a computing device, the method comprising:
forming a trust region within a search space based on computing a recursive specification vector defining the trust region;
computing a recursive shadow-impulse-response vector that lies substantially within the trust region; and
computing the approximate impulse-response vector based on the recursive shadow-impulse-response vector and the recursive specification vector.

2. The method of claim 1 wherein the search space further comprises a set of possible approximate impulse-response vectors centered at the origin in □L with a radius of √{square root over (E)}, where E represents the maximum amplification energy, or gain, produced by a microphone located in the first location in response to an impulse, and L is a positive integer.

3. The method of claim 1 wherein the trust region further comprise a hyper-dimensional geometric region within the search space.

4. The method of claim 1 wherein computing a recursive specification vector further comprises employing a recursive formula for the specification vector given by:


{right arrow over (Λ)}(m)=(1−η){right arrow over (Λ)}(m-1)+η{right arrow over (ĥ)}(m-1)∘{right arrow over (ĥ)}(m-1) 


where m is an integer associated with a decision period,
{right arrow over (Λ)}(m-1) is the hyper-ellipsoid-specification vector associate with a previous decision period identified by m−1,
{right arrow over (ĥ)}(m-1) is an impulse-response vector associated with a previous decision period identified by m−1,
∘ represents component wise multiplication, and
η is a weighting factor.

5. The method of claim 1 wherein computing the recursive shadow-impulse-response vector further comprises employing a recursive formula for the shadow-impulse-response vector given by:


{right arrow over ({tilde over (h)})}(m)={right arrow over ({tilde over (h)})}(m-1)+μm{right arrow over ({tilde over (ε)})}(m) 


where {right arrow over ({tilde over (ε)})}(m) is a shadow-mismatch vector,
{right arrow over ({tilde over (h)})}(m-1) is a shadow-impulse-response vector associated with a previous decision period identified by m−1, and
μm is a shadow update step size.

6. The method of claim 5 wherein the shadow-mismatch vector further comprises:




  
    
      
        ɛ
        _
      
      ~
    
    
      (
      m
      )
    
  
  =
  
    
      
        Tr
        L
      
      ·
      IFFT
    
    ⁢
    
      {
      
        
          
            Q
            _
          
          
            (
            m
            )
          
        
        ·
        
          
            X
            _
          
          
            (
            m
            )
          
        
        ·
        
          
            (
            
              
                
                  R
                  _
                
                ~
              
              
                (
                m
                )
              
            
            )
          
          *
        
      
      }
    
  




where m is an integer associated with a decision period,
L is a number of vector components,
IFFT is the inverse Fourier transform operator,
TrL is a truncation operator of size L,
{right arrow over (Q)}(m) is a frequency domain, preconditioning operator,
{right arrow over (X)}(m) is a frequency domain vector corresponding to the audio signal, and
{right arrow over ({tilde over (R)})}(m) is a frequency domain, shadow error vector.

7. The method of claim 6 wherein components of the frequency domain, preconditioning operator further comprise:




  
    
      Q
      
        (
        m
        )
      
    
    ⁡
    
      [
      k
      ]
    
  
  =
  
    1
    
      max
      ⁢
      
        {
        
          
            
              
                S
                xx
                
                  (
                  m
                  )
                
              
              ⁡
              
                [
                k
                ]
              
            
            +
            
              
                α
                m
              
              ⁢
              
                
                  S
                  
                    
                      r
                      ~
                    
                    ⁢
                    
                      r
                      ~
                    
                  
                  
                    (
                    m
                    )
                  
                
                ⁡
                
                  [
                  k
                  ]
                
              
            
          
          ,
          λ
        
        }
      
    
  




where Sxx(m)[k] is a component of an average spectrum of the frequency domain vector {right arrow over (X)}(m) given by {right arrow over (S)}xx(m)=(1−β){right arrow over (S)}xx(m-1)+β{right arrow over (X)}(m)∘{right arrow over (X)}(m),
S{tilde over (r)}{tilde over (r)}(m)[k] is a component of an average spectrum of the frequency domain shadow error vector {right arrow over ({tilde over (R)})}(m) given by {right arrow over (S)}{tilde over (r)}{tilde over (r)}(m)=(1−β){right arrow over (S)}{tilde over (r)}{tilde over (r)}(m-1)+β{right arrow over ({tilde over (R)})}(m)∘{right arrow over ({tilde over (R)})}(m),
λ is a stabilizing constant, and





  
    α
    m
  
  =
  
    5
    ⁢
    
      
        (
        
          
            E
            
              r
              ~
            
            
              2
              ⁢
              
                (
                m
                )
              
            
          
          
            E
            
              r
              ^
            
            
              2
              ⁢
              
                (
                m
                )
              
            
          
        
        )
      
      4
    
    ⁢
    
      
        
          
            σ
            .
          
          x
          
            2
            ⁢
            
              (
              m
              )
            
          
        
        
          M
          x
          
            2
            ⁢
            
              (
              m
              )
            
          
        
      
      .

8. The method of claim 7 wherein




  
    
      
        
          
            E
            
              r
              ~
            
            
              2
              ⁢
              
                (
                m
                )
              
            
          
          =
          
            
              1
              
                N
                d
              
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  0
                
                
                  
                    N
                    d
                  
                  -
                  1
                
              
              ⁢
              
                
              
              ⁢
              
                
                  
                  
                    
                      r
                      ~
                    
                    ⁡
                    
                      (
                      
                        
                          mN
                          d
                        
                        -
                        i
                      
                      )
                    
                  
                  
                
                2
              
            
          
        
        ,
      
    
  
  
    
      
        
          
            E
            
              r
              ^
            
            
              2
              ⁢
              
                (
                m
                )
              
            
          
          =
          
            
              1
              
                N
                d
              
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  0
                
                
                  
                    N
                    d
                  
                  -
                  1
                
              
              ⁢
              
                
              
              ⁢
              
                
                  
                  
                    
                      r
                      ^
                    
                    ⁡
                    
                      (
                      
                        
                          mN
                          d
                        
                        -
                        i
                      
                      )
                    
                  
                  
                
                2
              
            
          
        
        ,
      
    
  
  
    
      
        
          
            
              
                σ
                .
              
              x
              
                2
                ⁢
                
                  (
                  m
                  )
                
              
            
            ⁡
            
              [
              n
              ]
            
          
          =
          
            
              0.8
              ⁢
              
                
                  
                    σ
                    .
                  
                  x
                  
                    2
                    ⁢
                    
                      (
                      
                        m
                        -
                        1
                      
                      )
                    
                  
                
                ⁡
                
                  [
                  n
                  ]
                
              
            
            +
            
              0.2
              ⁢
              
                E
                x
                
                  2
                  ⁢
                  
                    (
                    m
                    )
                  
                
              
            
          
        
        ,
        and
      
    
  



Mx2(m) is a maximum energy associated with the audio signal.

9. The method of claim 6 wherein the frequency domain, shadow error vector {right arrow over ({tilde over (R)})}(m) further comprises:




  
    
      R
      
        ⇀
        ~
      
    
    
      (
      m
      )
    
  
  =
  
    
      FFT
      ·
      
        Tr
        p
      
      ·
      IFFT
    
    ⁢
    
      {
      
        
          
            Y
            ⇀
          
          
            (
            m
            )
          
        
        -
        
          
            
              
                X
                ⇀
              
              0
              
                (
                m
                )
              
            
            (
            
              
                H
                
                  ⇀
                  ~
                
              
              
                (
                
                  m
                  -
                  1
                
                )
              
            
            )
          
          *
        
      
      }
    
  




where FFT is the fast Fourier transform operator,
TrP is a truncation operator of length P,
IFFT is the inverse fast Fourier transform operator,
{right arrow over (Y)}(m) is a frequency domain vector corresponding to an audio signal with an acoustic echo transmitted from the second location to the first location, and
{right arrow over ({tilde over (H)})}(m-1) is a frequency domain shadow-impulse-response vector.

10. The method of claim 5 wherein the shadow-update-step size μm further comprises setting


μm=0.2


when μ_scale(m)>1, otherwise




  
    μ
    m
  
  =
  
    0.2
    
      
        μ_scale
        
          (
          m
          )
        
      
    
  




where




  
    μ_scale
    
      (
      m
      )
    
  
  =
  
    
      ∑
      
        n
        =
        0
      
      
        L
        -
        1
      
    
    ⁢
    
      
    
    ⁢
    
      
        
          (
          
            
              
                ɛ
                ~
              
              
                (
                m
                )
              
            
            ⁡
            
              [
              n
              ]
            
          
          )
        
        2
      
      
        
          Λ
          
            (
            m
            )
          
        
        ⁡
        
          [
          n
          ]
        
      
    
  




{tilde over (ε)}(m)[n] is the nth element of the shadow-mismatch vector {right arrow over ({tilde over (ε)})}(m), and Λ(m)[n] is the nth element of a hyper-ellipsoid-specification vector {right arrow over (Λ)}(m).

11. The method of claim 1 wherein computing the approximate impulse-response vector based on the recursive shadow-impulse-response vector and the recursive specification vector further comprises employing a recursive formula given by:


{right arrow over (ĥ)}(m)=(1−γm){right arrow over (ĥ)}(m-1)+γm{right arrow over ({tilde over (h)})}(m) 


where {right arrow over ({tilde over (h)})}(m) is a shadow-impulse-response vector associated with a decision period identified by m,
{right arrow over (ĥ)}(m-1) is an approximate impulse-response vector associated with a previous decision period identified by m−1, and
γm is an impulse response step size.

12. The method of claim 11 wherein the impulse response step size γm further comprises setting




  
    γ
    m
  
  =
  
    
      γ
      m
    
    
      
        μ_scale
        
          (
          m
          )
        
      
    
  




when μ_scale(m)>1, where




  
    
      γ_scale
      
        (
        m
        )
      
    
    =
    
      
        1
        L
      
      ⁢
      
        
          ∑
          
            n
            =
            0
          
          L
        
        ⁢
        
          
        
        ⁢
        
          
            
              (
              
                
                  
                    h
                    ~
                  
                  
                    (
                    m
                    )
                  
                
                ⁡
                
                  [
                  n
                  ]
                
              
              )
            
            2
          
          
            
              Λ
              
                (
                m
                )
              
            
            ⁡
            
              [
              n
              ]
            
          
        
      
    
  
  ,




{tilde over (h)}(m)[n] is the nth element of the shadow-impulse vector {right arrow over ({tilde over (h)})}(m), and Λ(m)[n] is the nth element of a hyper-ellipsoid-specification vector {right arrow over (Λ)}(m).

13. The method of claim 11 wherein the impulse response step size γm further comprises computing:




  
    γ
    m
  
  =
  
    
      (
      
        
          α
          m
        
        
          
            α
            m
          
          +
          
            c
            m
          
        
      
      )
    
    .85
  




where




  
    
      α
      m
    
    =
    
      5
      ⁢
      
        
          (
          
            
              E
              
                r
                ~
              
              
                2
                ⁢
                
                  (
                  m
                  )
                
              
            
            
              E
              
                r
                ^
              
              
                2
                ⁢
                
                  (
                  m
                  )
                
              
            
          
          )
        
        4
      
      ⁢
      
        
          
            σ
            .
          
          x
          
            2
            ⁢
            
              (
              m
              )
            
          
        
        
          M
          x
          
            2
            ⁢
            
              (
              m
              )
            
          
        
      
    
  
  ,
  and




for M decision periods and E{tilde over (r)}2≦0.9E{circumflex over (r)}2,


cm=max{cm-1−4000,400},


otherwise


cm=max{cm-1+1,40000}

14. A method of canceling an acoustic echo in an audio signal transmitted from a first location to a second location using a computing device, the method comprising:
computing a plurality of impulse-response vectors and associated echo-return-loss-enhancement values;
selecting an impulse-response vector from among the plurality of impulse response vectors when audio signals are transmitted between the first location and the second location; and
generating an output digital signal at the first location based on subtracting an approximate acoustic echo from an audio signal produced at the second location, the approximate acoustic echo depending on the impulse-response vector.

15. The method of claim 14 wherein each echo-return-loss-enhancement value is greater than a threshold value and is computed by:




  
    ERLE
    
      (
      
        m
        i
      
      )
    
  
  =
  
    10
    ⁢
    
      
    
    ⁢
    
      
        log
        10
      
      ⁡
      
        (
        
          
            
              
                σ
                .
              
              y
              
                2
                ⁢
                
                  (
                  
                    m
                    i
                  
                  )
                
              
            
            ⁡
            
              [
              n
              ]
            
          
          
            
              
                σ
                .
              
              
                r
                ^
              
              
                2
                ⁢
                
                  (
                  
                    m
                    i
                  
                  )
                
              
            
            ⁡
            
              [
              n
              ]
            
          
        
        )
      
    
  



{dot over (σ)}y2(mi)[n] is short term energy variance for a signal transmitted from the second location to the first location,
{dot over (σ)}{circumflex over (r)}2(mi)[n] is short term energy variance for a shadow residual signal, and
mi is a decision period.

16. The method of claim 14 wherein selecting the impulse-response vector from among the plurality of impulse-response vectors further comprises selecting the impulse-response vector with the largest associated echo-return-loss-enhancement value.

17. The method of claim 14 wherein selecting the impulse-response vector from the data structure further comprises selecting the impulse-response vector that has been among the plurality of impulse-response vectors for the longest period of time.

18. The method of claim 14 wherein generating the output digital signal further comprises calculating:




  
    
      
        
          r
          ⇀
        
        ^
      
      
        (
        m
        )
      
    
    ⁡
    
      [
      n
      ]
    
  
  =
  
    
      
        Tr
        
          N
          d
        
      
      ·
      IFFT
    
    ⁢
    
      {
      
        
          
            Y
            ⇀
          
          
            (
            m
            )
          
        
        -
        
          
            
              
                X
                ⇀
              
              0
              
                (
                m
                )
              
            
            ⁡
            
              (
              
                
                  
                    H
                    ⇀
                  
                  ^
                
                
                  (
                  
                    m
                    -
                    1
                  
                  )
                
              
              )
            
          
          *
        
      
      }
    
  




where m is an integer associated with a decision period,
Nd is the length of the decision period,
TrNd is a truncation operator of length Nd,
IFFT is the inverse fast Fourier transform,
{right arrow over (Y)}(m) is a frequency domain signal transmitted from the second location to the first location,
{right arrow over (X)}(m) is a frequency domain signal transmitted from the first location to the second location, and
{right arrow over (Ĥ)}(m-1) is a frequency domain impulse-response vector associated with a previous decision period m−1.

19. A method of updating a data structure of approximate impulse-response vectors using a computing device, the method comprising:
computing a plurality of approximate impulse-response vectors and associated echo-return-loss-enhancement values;
storing a first approximate impulse-response vector in the data structure when the corresponding echo-return-loss-enhancement value is greater than a threshold value; and
deleting a second approximate impulse-response vector in the data structure.

20. The method of claim 19 wherein the echo-return-loss-enhancement value further comprises:




  
    ERLE
    
      (
      m
      )
    
  
  =
  
    10
    ⁢
    
      
    
    ⁢
    
      
        log
        10
      
      ⁡
      
        (
        
          
            
              
                σ
                .
              
              y
              
                2
                ⁢
                
                  (
                  m
                  )
                
              
            
            ⁡
            
              [
              n
              ]
            
          
          
            
              
                σ
                .
              
              
                r
                ^
              
              
                2
                ⁢
                
                  (
                  m
                  )
                
              
            
            ⁡
            
              [
              n
              ]
            
          
        
        )
      
    
  




where
{dot over (σ)}y2(m)[n] is short term energy variance for a signal transmitted from the second location to the first location, and
{dot over (σ)}{circumflex over (r)}2(m)[n] is short term energy variance for a shadow residual signal.

21. The method of claim 19 wherein deleting a second approximate impulse-response vector from the data structure further comprises deleting an approximate impulse-response vector from the data structure with the smallest associated echo-return-loss-enhancement value.

22. The method of claim 19 wherein deleting a second approximate impulse-response vector from the data structure further comprises deleting an approximate impulse-response vector from the data structure that has been stored in the data structure for the longest period of time.