Abstract:
An apparatus for canceling an acoustic echo signal caused by a far-end talker signal is provided. The apparatus for canceling an acoustic echo signal includes: a variance estimating unit configured to estimate a variance of a first audio signal of a near-end talker signal and a first noise signal of the near-end talker signal; a step size determining unit configured to determine a step size by using the variance of the first audio signal and the variance of the first noise signal; an adaptive filter coefficient updating unit configured to update an adaptive filter coefficient of an adaptive filter by using the step size; and an acoustic echo canceling unit configured to estimate an acoustic echo signal by using the adaptive filter coefficient, and cancel the acoustic echo signal from a microphone input signal by using the estimated acoustic echo signal.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority to and the benefit of Korean Patent Application No. 10-2012-0118124 and 10-2013-0118051 filed in the Korean Intellectual Property Office on Oct. 23, 2012 and Oct. 2, 2013, the entire contents of which are incorporated herein by reference. 
       BACKGROUND OF THE INVENTION 
       [0002]    (a) Field of the Invention 
         [0003]    The present invention relates to a method and apparatus for canceling an acoustic echo signal. 
         [0004]    (b) Description of the Related Art 
         [0005]    An acoustic echo canceller (AEC) is a device that re-inputs an audio signal output from a speaker to a microphone directly or indirectly (through reflection from a wall or a peripheral object) in a video call, a video conference, or the like, to thus cancel acoustic echo, which is the repetition of a sound of a user. In canceling acoustic echo with an AEC, it is very important to accurately estimate an acoustic echo generation path (or a room impulse response (RIR)). In general, the AEC estimates the acoustic echo generation path (or RIR) by using an adaptive filter, and generates an estimated acoustic echo signal. Thereafter, the AEC subtracts the estimated acoustic echo signal from an actual acoustic echo signal, thus canceling acoustic echo. 
         [0006]    A method of updating an adaptive filter coefficient of an adaptive filter for estimating an acoustic echo generation path (or RIR) includes a method of using a recursive least squares (RLS) algorithm, a method of using a least mean square (LMS) algorithm, a method of using a normalized least mean square (NLMS) algorithm, a method of using an affine projection algorithm, and the like. Each updating method is implemented even in a frequency domain and a sub-band domain, as well as in a time domain. Most AECs use the NLMS algorithm due to a small amount of calculation and ease in implementation. Meanwhile, in a case of updating an adaptive filter coefficient, the NLMS algorithm requires a step size parameter. If a step size is large, an acoustic echo generation path may be more promptly estimated, but a difference between the estimated acoustic echo generation path and an actual acoustic echo generation path is increased. Conversely, if a step size is small, an acoustic echo generation path may be more accurately estimated, but more time is required for estimation. Thus, in order to enhance both a convergence speed as to how fast an estimated acoustic echo generation path is converged on an actual acoustic echo generation path and accuracy of the estimated acoustic echo signal, a step size is required to be variably controlled. Various methods of variably controlling a step size have been proposed. 
         [0007]    Recently, Qualcomm has proposed a method of adjusting a step size resistant to double torque by estimating energy of a noise signal and an audio signal of a near-end talker signal in a time domain through U.S. Patent Laid-Open Publication No. 2010/0057454. Meanwhile, Yin Zhou and Xiaodong Li presented a method of controlling a step size in a frequency domain such that increments of errors (adaptive filter mismatch errors) between an adaptive filter coefficient and an actual acoustic echo generation path are minimized, in an article entitled “A variable step-size for frequency-domain acoustic echo cancellation”. 
         [0008]    However, the foregoing related arts have a problem in that, when an actual acoustic echo generation path is changed over time, an adaptive filter coefficient cannot quickly follow the actual acoustic echo generation path in a frequency domain. 
         [0009]    The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art. 
       SUMMARY OF THE INVENTION 
       [0010]    The present invention has been made in an effort to provide a method for controlling a step size in a frequency domain. 
         [0011]    The present invention has also been made in an effort to provide a step size controlling method by which an adaptive filter coefficient is quickly adaptable to an actual acoustic echo generation path even though the actual acoustic echo generation path is changed over time. 
         [0012]    The present invention has also been made in an effort to provide an acoustic echo canceling method and apparatus using a variable step size. 
         [0013]    An exemplary embodiment of the present invention provides an apparatus for canceling an acoustic echo signal caused by a far-end talker signal. The apparatus for canceling an acoustic echo signal may include: a variance estimating unit configured to estimate a variance of a first audio signal of a near-end talker signal and a first noise signal of the near-end talker signal; a step size determining unit configured to determine a step size by using the variance of the first audio signal and the variance of the first noise signal; an adaptive filter coefficient updating unit configured to update an adaptive filter coefficient of an adaptive filter by using the step size; and an acoustic echo canceling unit configured to estimate an acoustic echo signal by using the adaptive filter coefficient, and cancel the acoustic echo signal from a microphone input signal by using the estimated acoustic echo signal generated through the estimation of the acoustic echo signal. The step size determining unit may determine the step size such that a first residual signal is equal to the near-end talker signal. The first residual signal may be a signal obtained by subtracting a first estimated acoustic echo signal as the estimated acoustic echo signal from the microphone input signal 
         [0014]    The first estimated acoustic echo signal may be a signal obtained by using the adaptive filter coefficient updated. 
         [0015]    The variance estimating unit may estimate the variance of the first noise signal and the variance of the first audio signal by using the probability of presence of the acoustic echo signal. 
         [0016]    The variance estimating unit may estimate the variance of the first noise signal and the variance of the first audio signal by using the probability that a second audio signal will exist in the far-end talker signal. 
         [0017]    The variance estimating unit may use a first probability that only a second noise signal will exist in the far-end talker signal in a frequency domain and a second probability that the second audio signal and the second noise signal will exist in the far-end talker signal in the frequency domain. 
         [0018]    The variance estimating unit may estimate a first sum as the sum of the variance of the first noise signal and the variance of the first audio signal through smoothing. 
         [0019]    The variance estimating unit may calculate the first sum by using a variance of the acoustic echo signal. 
         [0020]    The second audio signal and the second noise signal may be statistically independent from one another. 
         [0021]    The step size determining unit may determine the step size by using the sum of the variance of the first audio signal and the variance of the first noise signal. 
         [0022]    The adaptive filter coefficient updating unit may use a normalized least mean square (NLMS) algorithm in a frequency domain. 
         [0023]    Another embodiment of the present invention provides a method of canceling an acoustic echo signal caused by a far-end talker signal by an acoustic echo canceller. The method of canceling acoustic echo may include: estimating a variance of a first audio signal of a near-end talker signal and a first noise signal of the near-end talker signal; determining a step size by using the variance of the first audio signal and the variance of the first noise signal; updating an adaptive filter coefficient of an adaptive filter by using the step size; generating an estimated acoustic echo signal corresponding to the acoustic echo signal by using the adaptive filter coefficient; and canceling the acoustic echo signal from a microphone input signal by using the estimated acoustic echo signal. In the determining, the step size is determined such that a first residual signal is equal to the near-end talker signal. The first residual signal is a signal obtained by subtracting a first estimated acoustic echo signal as the estimated acoustic echo signal from the microphone input signal. When a path (a room impulse response (RIR)) for generating the first acoustic echo signal is modeled by a filter, and the adaptive filter coefficient may correspond to a filter coefficient of the filter. 
         [0024]    Yet another embodiment of the present invention provides a method of updating an adaptive filter coefficient by an acoustic echo canceller including an adaptive filter. The method for updating an adaptive filter coefficient may include: 
         [0025]    estimating a first variance sum as the sum of a variance of an audio signal of a near-end talker signal and a variance of a noise signal of the near-end talker signal; 
         [0026]    determining a step size by using the first variance sum; and 
         [0027]    updating the adaptive filter coefficient by using the step size. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0028]      FIG. 1  is a view illustrating a process of canceling acoustic echo by a general acoustic echo canceller in a time domain. 
           [0029]      FIG. 2  is a view illustrating a process of canceling acoustic echo by the general acoustic echo canceller in a frequency domain. 
           [0030]      FIG. 3  is a view illustrating a process of determining a step size according to an embodiment of the present invention. 
           [0031]      FIG. 4  is a view illustrating a process of estimating variances of an audio signal and a noise signal of a near-end talker signal according to an embodiment of the present invention. 
           [0032]      FIG. 5  is a view illustrating a process of canceling acoustic echo by an acoustic echo canceller according to an embodiment of the present invention. 
           [0033]      FIG. 6  is a block diagram of an acoustic echo canceller according to an embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       [0034]    In the following detailed description, only certain exemplary embodiments of the present invention have been shown and described, simply by way of illustration. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. Accordingly, the drawings and description are to be regarded as illustrative in nature and not restrictive. Like reference numerals designate like elements throughout the specification. 
         [0035]      FIG. 1  is a view illustrating a process of canceling acoustic echo by a general acoustic echo canceller in a time domain. 
         [0036]    An audio signal (s(n)) of a near-end talker signal and a noise signal (v(n)) of the near-end talker signal at a time n are input to a microphone. 
         [0037]    Meanwhile, a far-end talker signal (f(n)) output from a speaker at a time n is input to a filter  10 . Here, the filter  10  is a virtual filter which has modeled an actual acoustic echo generation path (or RIR), and it is assumed that the filter  10  has a filter coefficient ({right arrow over (w)}(n)). An actual acoustic echo signal (y(n)) at the time is generated by the filter  10 , is input to the microphone. As a result, microphone input signals input to the near-end talker microphone at the time n are s(n)+v(n)+y(n). 
         [0038]    An adaptive filter  20  estimates the actual acoustic echo signal (y(n)) by using the far-end talker signal (f(n)) to generate an estimated acoustic echo signal (ŷ(n)). Here, the adaptive filter  20 , which corresponds with the filter  10 , has an adaptive filter coefficient ({circumflex over ({right arrow over (w)}(n)). 
         [0039]    When the estimated acoustic echo signal (ŷ(n)) is subtracted from the microphone input signal (d(n)), a residual signal (e(n)) is generated. As a result, the residual signal is a signal without acoustic echo. 
         [0040]      FIG. 2  is a view illustrating a process of canceling acoustic echo by the general acoustic echo canceller in a frequency domain. In  FIG. 2 , a case in which acoustic echo is canceled by using an overlap-save method is shown. 
         [0041]    A far-end talker signal vector ({circumflex over (x)}(k)) of a k th frame and a microphone input signal vector ({right arrow over (d)}(k)) are defined as represented by Equation 1 below. 
         [0000]        {right arrow over (x)} ( k )=[ f ( kN−N ), . . . , f ( kN− 1), f ( kN ), . . . , f ( kN+N− 1)] T    
         [0000]        {right arrow over (d)} ( k )=[ d ( kN ), . . . , d ( kN+N− 1)] T   [Equation 1]
 
         [0042]    Here, N is a natural number representing a frame size, and [ ] T  is a transposed matrix. 
         [0043]    When the far-end talker signal vector ({right arrow over (x)}(k)) is converted into a frequency domain (S 100 ), a far-end talker signal matrix (X(k)) in the frequency domain may be represented by Equation 2 below. 
         [0000]        X ( k )=diag{ F{right arrow over (x)} ( k )}  [Equation 2]
 
         [0044]    In Equation 2, F is a 2N×2N discrete Fourier transform (DFT) matrix, and diag{·} is an operator generating a diagonal matrix. 
         [0045]    An adaptive filter coefficient vector ({circumflex over ({right arrow over (w)}(k)) of the k th frame is defined as represented by Equation 3 below. Here, the adaptive filter coefficient vector ({circumflex over ({right arrow over (w)}(k)) represents an acoustic echo path estimated in the time domain. 
         [0000]        {circumflex over ({right arrow over (w)} ( k )=[ ŵ   0 ( k ), . . . , ŵ   N-1 ( k )] T   [Equation 3]
 
         [0046]    When number of 0s are added behind the adaptive filter coefficient vector ({circumflex over ({right arrow over (w)}(k)) and converted into the frequency domain, an adaptive filter coefficient vector ({circumflex over ({right arrow over (W)}(k)) in the frequency domain may be represented by Equation 4 below. 
         [0000]        {circumflex over ({right arrow over (W)} ( k )= FL   T   {circumflex over ({right arrow over (w)} ( k )  [Equation 4]
 
         [0047]    Here, L is [I N O N ], O N  is an N×N matrix in which all the values are 0, and I N  is an N×N identity matrix. 
         [0048]    An acoustic echo signal vector ({circumflex over ({right arrow over (Y)}(k)) is generated by multiplying the far-end talker signal matrix (X(k)) by the adaptive filter coefficient vector ({circumflex over ({right arrow over (W)}(k)) (S 101 ). That is, the estimated acoustic echo signal vector ({circumflex over ({right arrow over (Y)}(k)) is represented by Equation 5 below. 
         [0000]        {circumflex over ({right arrow over (Y)} ( k )= X ( k ) {circumflex over ({right arrow over (W)} ( k )  [Equation 5]
 
         [0049]    The acoustic echo signal vector ({circumflex over ({right arrow over (y)}(k)) estimated in the time domain is obtained by performing IDFT (inverse discrete Fourier transform) on the estimated acoustic echo signal vector ({circumflex over ({right arrow over (Y)}(k)) (S 102 ) and subsequently selecting only N number of final components (S 103 ). That is, the estimated acoustic echo signal vector ({circumflex over ({right arrow over (y)}(k)) is represented by Equation 6 below. 
         [0000]        {circumflex over ({right arrow over (y)} ( k )= RF   −1   {circumflex over ({right arrow over (Y)} ( k )  [Equation 6]
 
         [0050]    Here, R is [O N I N ]. 
         [0051]    The residual signal vector ({right arrow over (E)} pri (k)) is obtained by obtaining a difference between the microphone input signal vector ({right arrow over (d)}(k)) and the estimated acoustic echo signal vector ({circumflex over ({right arrow over (y)}(k)) (S 104 ), adding the number of 0s (S 105 ), and converting the same into a frequency domain (S 106 ). That is, the residual signal vector ({right arrow over (E)} pri (k)) may be represented by Equation 7 below. 
         [0000]        {right arrow over (E)}   pri ( k )= FR   T ( {right arrow over (d)} ( k )− {circumflex over ({right arrow over (y)} ( k ))  [Equation 7]
 
         [0052]    When a step size in an m-th frequency bin is defined as μ m (k) and power of the m-th frequency bin is defined as P m (k), a normalized step size matrix (u(k)) and power matrix Λ(k)) of the far-end talker signal are represented by Equation 8 below. 
         [0000]        u ( k )=diag{μ 0 ( k ), . . . ,μ 2N-1 ( k )}
 
         [0000]      Λ( k )=diag{ P   0 ( k ), . . . , P   2N-1 ( k )}  [Equation 8]
 
         [0053]    The adaptive filter coefficient vector ({circumflex over ({right arrow over (W)}(k)) is updated through operations S 107  to S 116 . That is, the adaptive filter coefficient vector ({circumflex over ({right arrow over (W)}(k)) is updated as shown in Equation 9 below. 
         [0000]        {circumflex over ({right arrow over (W)} ( k+ 1)= {circumflex over ({right arrow over (W)} ( k )+2 Gu ( k )Λ −1 ( k ) X   H ( k ) {right arrow over (E)}   pri ( k )  [Equation 9]
 
         [0054]    Here, G is FgF −1 , and g is 
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         [0000]    {circumflex over ({right arrow over (W)}(k+1) represents an updated adaptive filter coefficient vector. Λ −1 (k) is obtained through a power calculation and reciprocal calculation operation (S 109 ). X H (k) is obtained through a complex conjugate calculation operation (S 107 ). X H (k)           During the operations S 111  to S 114 , the signal obtained through the operation S 110  is converted into frequency domain→time domain→frequency domain. 
         [0055]      FIG. 3  is a view illustrating a process of determining a step size according to an embodiment of the present invention. A step size (u(k)) is used to regulate updating of the adaptive filter coefficient vector ({circumflex over ({right arrow over (W)}(k)) in the frequency domain. 
         [0056]    The microphone input signal vector ({right arrow over (d)}(k)) in the time domain includes a noise signal vector ({right arrow over (v)}(k)) of the near-end talker signal, an audio signal vector ({right arrow over (s)}(k)) of the near-end talker signal, and an acoustic echo signal vector ({right arrow over (y)}(k)). Here, the noise signal vector ({right arrow over (v)}(k)) and the audio signal vector ({right arrow over (s)}(k)) are statistically independent from one another. The noise signal vector ({right arrow over (V)}(k)) of the near-end talker signal and the audio signal vector ({right arrow over (S)}(k)) of the near-end talker signal in the frequency domain are represented by Equation 10 below. Equation 10 corresponds to operations S 205 , S 206 , S 208 , and S 209 . 
         [0000]        {right arrow over (V)} ( k )=[ V   0 ( k ), . . . , V   N-1 ( k )] T   =FR   T   {right arrow over (v)} ( k ) 
         [0000]        {right arrow over (S)} ( k )=[ S   0 ( k ), . . . , S   N-1 ( k )] T   =FR   T   {right arrow over (s)} ( k )  [Equation 10]
 
         [0057]    A pre-residual signal vector ({right arrow over (E)} pri (k)) obtained by using the adaptive filter coefficient vector ({circumflex over ({right arrow over (W)}(k)) is obtained through operations S 200  to S 230 . That is, the pre-residual signal vector ({right arrow over (E)} pri (k)) is represented by Equation 11 below. 
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         [0058]    Here, {tilde over (G)} is F{tilde over (g)}F −1 , and {tilde over (g)} is 
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         [0000]    {right arrow over (W)}(k) is obtained by converting the filter coefficient ({right arrow over (w)}(n)) of the filter  10  in the time domain into a frequency domain. 
         [0059]    Meanwhile, a post-residual signal vector ({right arrow over (E)} post (k)) obtained by using an updated adaptive filter coefficient vector ({circumflex over ({right arrow over (W)}(k+1)) is represented by Equation 12 below. 
         [0000]        {right arrow over (E)}   post ( k )= {tilde over (G)}X ( k )( {right arrow over (W)} ( k )− {circumflex over ({right arrow over (W)} ( k+ 1))+ {right arrow over (V)} ( k )+ {right arrow over (S)} ( k )  [Equation 12]
 
         [0060]    A difference between the pre-residual signal vector ({right arrow over (E)} pri (k)) and the post-residual signal vector ({right arrow over (E)} post (k)) is obtained as expressed by Equation 13 below. 
         [0000]        {right arrow over (E)}   post ( k )= {right arrow over (E)}   pri ( k )+ {tilde over (G)}X ( k )( {circumflex over ({right arrow over (W)} ( k )− {circumflex over ({right arrow over (W)} ( k+ 1))  [Equation 13]
 
         [0061]    A step size (u(k)) is determined such that the post-residual signal vector is equal to {right arrow over (V)}(k)+{right arrow over (S)}(k). When Equation 9 is applied to Equation 13 and solved, Equation 14 may be obtained. 
         [0000]        {right arrow over (V)} ( k )+ {right arrow over (S)} ( k )= {right arrow over (E)}   pri ( k )−2 {tilde over (G)}X ( k ) Gu ( k )Λ −1 ( k ) X   H ( k ) {right arrow over (E)}   pri ( k )  [Equation 14]
 
         [0062]    When it is assumed that different frequency bins are independent from each other, a step size (μ m (k)) may be independently determined in each m-th frequency bin from Equation 15 below. 
         [0000]        V   m ( k )+ S   m ( k )= E   pri,m ( k )−2 {right arrow over (j)}   m   {tilde over (G)}X ( k ) Gu ( k )Λ −1 ( k ) X   H ( k ) {right arrow over (E)}   pri ( k )  [Equation 15]
 
         [0063]    Here, {right arrow over (j)} m  is a 1×2N vector in which only the m-th element value is 1 and the remaining element values are 0. 
         [0064]    When both sides of Equation 15 are squared and averaged, Equation 16 below is obtained. 
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                                 1 
                               
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                           
                             
                               u 
                               H 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                           
                             G 
                             H 
                           
                            
                           
                             
                               X 
                               H 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                           
                             
                               G 
                               ~ 
                             
                             H 
                           
                            
                           
                             
                               j 
                               → 
                             
                             m 
                             H 
                           
                            
                           
                             
                               j 
                               → 
                             
                             m 
                           
                            
                           
                             G 
                             ~ 
                           
                            
                           
                             X 
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                           
                             Gu 
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                           
                             
                               Λ 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                           
                             
                               X 
                               H 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                           
                             
                               
                                 E 
                                 → 
                               
                               pri 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     16 
                   
                   ] 
                 
               
             
           
         
       
     
         [0065]    Here, Re[ ] is a real part of a complex number, and E* pri,m (k) is a complex conjugate of E pri,m (k). When Equation 16 is approximated with G≈I 2N /2, {tilde over (G)}≈I 2N /2, Equation 17 below is obtained. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                        
                       
                         { 
                         
                           
                              
                             
                               
                                 V 
                                 m 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                         } 
                       
                     
                     + 
                     
                       E 
                        
                       
                         { 
                         
                           
                              
                             
                               
                                 S 
                                 m 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                         } 
                       
                     
                   
                   = 
                   
                     
                       
                         E 
                          
                         
                           { 
                           
                             
                                
                               
                                 
                                   E 
                                   
                                     pri 
                                     , 
                                     m 
                                   
                                 
                                  
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           } 
                         
                       
                       + 
                       
                         
                           1 
                           4 
                         
                          
                         
                           
                             μ 
                             m 
                             2 
                           
                            
                           
                             ( 
                             k 
                             ) 
                           
                         
                          
                         E 
                          
                         
                           { 
                           
                             
                               
                                 
                                    
                                   
                                     
                                       X 
                                       
                                         m 
                                         , 
                                         m 
                                       
                                     
                                      
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                    
                                 
                                 4 
                               
                                
                               
                                 
                                    
                                   
                                     
                                       E 
                                       
                                         pri 
                                         , 
                                         m 
                                       
                                     
                                      
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                             
                             
                               
                                 P 
                                 m 
                                 2 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                       - 
                       
                         
                           
                             μ 
                             m 
                           
                            
                           
                             ( 
                             k 
                             ) 
                           
                         
                          
                         E 
                          
                         
                           { 
                           
                             
                               
                                 
                                    
                                   
                                     
                                       X 
                                       
                                         m 
                                         , 
                                         m 
                                       
                                     
                                      
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                                
                               
                                 
                                    
                                   
                                     
                                       E 
                                       
                                         pri 
                                         , 
                                         m 
                                       
                                     
                                      
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                             
                             
                               
                                 P 
                                 m 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                     
                     ≈ 
                     
                       
                         E 
                          
                         
                           { 
                           
                             
                                
                               
                                 
                                   E 
                                   
                                     pri 
                                     , 
                                     m 
                                   
                                 
                                  
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           } 
                         
                       
                       + 
                       
                         
                           1 
                           4 
                         
                          
                         
                           
                             μ 
                             m 
                             2 
                           
                            
                           
                             ( 
                             k 
                             ) 
                           
                         
                          
                         E 
                          
                         
                           { 
                           
                             
                                
                               
                                 
                                   E 
                                   
                                     pri 
                                     , 
                                     m 
                                   
                                 
                                  
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           } 
                         
                       
                       - 
                       
                         
                           
                             μ 
                             m 
                           
                            
                           
                             ( 
                             k 
                             ) 
                           
                         
                          
                         E 
                          
                         
                           { 
                           
                             
                                
                               
                                 
                                   E 
                                   
                                     pri 
                                     , 
                                     m 
                                   
                                 
                                  
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           } 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     17 
                   
                   ] 
                 
               
             
           
         
       
     
         [0066]    Here, X m,m (k) is a value present in an m-th row and an m-th column of the far-end talker signal matrix (X(k)). When a quadratic equation with respect to a step size (μ m (k)) is solved, Equation 18 is obtained. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         μ 
                         m 
                       
                        
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       2 
                        
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               
                                 
                                   E 
                                    
                                   
                                     { 
                                     
                                       
                                          
                                         
                                           
                                             V 
                                             m 
                                           
                                            
                                           
                                             ( 
                                             k 
                                             ) 
                                           
                                         
                                          
                                       
                                       2 
                                     
                                     } 
                                   
                                 
                                 + 
                                 
                                   E 
                                    
                                   
                                     { 
                                     
                                       
                                          
                                         
                                           
                                             S 
                                             m 
                                           
                                            
                                           
                                             ( 
                                             k 
                                             ) 
                                           
                                         
                                          
                                       
                                       2 
                                     
                                     } 
                                   
                                 
                               
                               
                                 E 
                                  
                                 
                                   { 
                                   
                                     
                                        
                                       
                                         
                                           E 
                                           
                                             pri 
                                             , 
                                             m 
                                           
                                         
                                          
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                        
                                     
                                     2 
                                   
                                   } 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     m 
                     = 
                     0 
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     N 
                     - 
                     1 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     18 
                   
                   ] 
                 
               
             
           
         
       
     
         [0067]    That is, the step size (μ m (k)) is determined by using a variance (E{|V m (k)| 2 }) of the noise signal of the near-end talker signal, a variance (E{|S m (k)| 2 }) of the audio signal of the near-end talker signal, and a variance (E{|E pri,m (k)| 2 }) of the residual signal. Equation 18 corresponds to operations S 204 , S 207 , and S 210  to S 216 . 
         [0068]      FIG. 4  is a view illustrating a process of estimating variances of an audio signal and a noise signal of a near-end talker signal according to an embodiment of the present invention. As described above, the variance (E{|E pri,m (k)| 2 }) of the residual signal, the variance (E{|V m (k)| 2 }) of the noise signal of the near-end talker signal, and the variance (E{|S m (k)| 2 }) of the audio signal of the near-end talker signal are required to obtain the step size (μ m (k)). In an embodiment of the present invention, variances of the audio signal and the noise signal of the near-end talker signal can be estimated on the basis of a statistical model in the frequency domain resistant to noise change over time. 
         [0069]    A square of the residual signal (E{|E pri,m (k)| 2 }) may be directly measured. Thus, the variance (E{|E pri,m (k)| 2 }) of the residual signal required for obtaining the step size (μ m (k)) may be estimated by performing a smoothing operation with a factor (β) having a value 0β&lt;1 as expressed in Equation 19 below. 
         [0000]        E{|E   pri,m ( k+ 1)| 2   }=βE{∥E   pri,m ( k )| 2 }+(1−β)| E   pri,m ( k )| 2   [Equation 19]
 
         [0070]    Meanwhile, unlike the variance (E{|E pri,m (k)| 2 }) of the residual signal, it is difficult to directly calculate the variance (E{|V m (k)| 2 }) of the noise signal of the near-end talker signal and the variance (E{|S m (k)| 2 }) of the audio signal of the near-end talker signal. In an embodiment of the present invention, the probability of presence of acoustic echo is calculated on the basis of a statistical model to estimate the variance (E{|V m (k)| 2 }) of the noise signal of the near-end talker signal and the variance (E{|S m (k)| 2 }) of the audio signal of the near-end talker signal. Hypotheses may be formulated for a case (H 0 ) in which the acoustic echo signal vector ({right arrow over (Y)}(k)) does not exist in the microphone input signal vector ({right arrow over (D)}(k)=[D 0 (k), . . . , D N-1 (k)] T ) and a case (H 1 ) in which it exists, in the frequency domain, as represented by Equation 20 below. 
         [0000]        H   0   :{right arrow over (D)} ( k )= {right arrow over (V)} ( k )+ {right arrow over (S)} ( k ) 
         [0000]        H   1   :{right arrow over (D)} ( k )= {right arrow over (V)} ( k )+ {right arrow over (S)} ( k )+ {right arrow over (Y)} ( k )  [Equation 20]
 
         [0071]    It is assumed that respective frequency bins are statistically independent from one another. Also, when it is assumed that the noise signal vector ({right arrow over (V)}(k)) of the near-end talker signal, the audio signal vector ({right arrow over (S)}(k)), and the acoustic echo signal vector ({right arrow over (Y)}(k)) are statistically independent from one another and a normal distribution has an average of 0, a probability distribution may be expressed by Equation 21 below. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                        
                       
                         ( 
                         
                           
                             
                               D 
                               m 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                           
                             H 
                             0 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         
                           π 
                            
                           
                             ( 
                             
                               
                                 σ 
                                 
                                   
                                     V 
                                     m 
                                   
                                   + 
                                   
                                     S 
                                     m 
                                   
                                 
                                 2 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                        
                       
                         exp 
                          
                         
                           [ 
                           
                             - 
                             
                               
                                 
                                    
                                   
                                     
                                       D 
                                       m 
                                     
                                      
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                               
                                 
                                   σ 
                                   
                                     
                                       V 
                                       m 
                                     
                                     + 
                                     
                                       S 
                                       m 
                                     
                                   
                                   2 
                                 
                                  
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       P 
                        
                       
                         ( 
                         
                           
                             
                               D 
                               m 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                           
                             H 
                             1 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         
                           π 
                            
                           
                             ( 
                             
                               
                                 
                                   σ 
                                   
                                     
                                       V 
                                       m 
                                     
                                     + 
                                     
                                       S 
                                       m 
                                     
                                   
                                   2 
                                 
                                  
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   σ 
                                   
                                     Y 
                                     m 
                                   
                                   2 
                                 
                                  
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                       
                        
                       
                         exp 
                          
                         
                           [ 
                           
                             - 
                             
                               
                                 
                                    
                                   
                                     
                                       D 
                                       m 
                                     
                                      
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                               
                                 
                                   
                                     σ 
                                     
                                       
                                         V 
                                         m 
                                       
                                       + 
                                       
                                         S 
                                         m 
                                       
                                     
                                     2 
                                   
                                    
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     σ 
                                     
                                       Y 
                                       m 
                                     
                                     2 
                                   
                                    
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     21 
                   
                   ] 
                 
               
             
           
         
       
     
         [0072]    Here, exp[ ] indicates an exponential function. However, since the near-end talker signal and the acoustic echo signal correspond to a voice, the two hypotheses (H 0 , H 1 ) have similar probability distributions. Thus, it is difficult to discriminate between the two hypotheses (H 0 , H 1 ) and obtain the probability of presence of an acoustic echo signal by using the probability distributions of Equation 21. That is, in order to discriminate between the two hypotheses (H 0 , H 1 ) by using the probability distributions, the probability distributions should be significant, but audio signals of the acoustic echo signal and the near-end talker signal are not sufficiently significant to be easily discriminated. 
         [0073]    In an embodiment of the present invention, instead of a probability that the acoustic echo signal vector ({right arrow over (Y)}(k)) will exist in the microphone input signal vector ({right arrow over (D)}(k)), a probability that an audio signal vector ({right arrow over (B)}(k)) will exist in the far-end talker signal vector ({right arrow over (X)}(k)=[X 0 (k), . . . , X N-1 (k)] T ) is used. Hypotheses may be formulated for a case) (H′ 0 ) in which the audio signal vector ({right arrow over (B)}(k)) does not exist in the far-end talker signal vector ({right arrow over (X)}(k)) and a case (H′ 1 ) in which it exists, in the frequency domain, as represented by Equation 22 below. 
         [0000]        H′   0   :{right arrow over (X)} ( k )= {right arrow over (N)} ( k ) 
         [0000]        H′   1   :{right arrow over (X)} ( k )= {right arrow over (N)} ( k )+ {right arrow over (B)} ( k )  [Equation 22]
 
         [0074]    Here, {right arrow over (N)}(k) is a noise signal vector of the far-end talker signal, and {right arrow over (B)}(k) is an audio signal vector of the far-end talker signal. 
         [0075]    Probability distributions of the two hypotheses (H′ 0 , H′ 1 ) are expressed by Equation 23 below. 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         P 
                          
                         
                           ( 
                           
                             
                               
                                 X 
                                 m 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                              
                             
                               H 
                               0 
                               ′ 
                             
                           
                           ) 
                         
                       
                       = 
                       
                         
                           1 
                           
                             
                               πσ 
                               
                                 N 
                                 m 
                               
                               2 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                          
                         
                           exp 
                            
                           
                             [ 
                             
                               - 
                               
                                 
                                   
                                      
                                     
                                       
                                         X 
                                         m 
                                       
                                        
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                 
                                   
                                     σ 
                                     
                                       N 
                                       m 
                                     
                                     2 
                                   
                                    
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       
                         P 
                          
                         
                           ( 
                           
                             
                               
                                 X 
                                 m 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                              
                             
                               H 
                               1 
                               ′ 
                             
                           
                           ) 
                         
                       
                       = 
                       
                         
                           1 
                           
                             π 
                              
                             
                               ( 
                               
                                 
                                   
                                     σ 
                                     
                                       N 
                                       m 
                                     
                                     2 
                                   
                                    
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     σ 
                                     
                                       B 
                                       m 
                                     
                                     2 
                                   
                                    
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                           
                         
                          
                         
                           exp 
                            
                           
                             [ 
                             
                               - 
                               
                                 
                                   
                                      
                                     
                                       
                                         X 
                                         m 
                                       
                                        
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                 
                                   
                                     
                                       σ 
                                       
                                         N 
                                         m 
                                       
                                       2 
                                     
                                      
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   + 
                                   
                                     
                                       σ 
                                       
                                         B 
                                         m 
                                       
                                       2 
                                     
                                      
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     23 
                   
                   ] 
                 
               
             
           
         
       
     
         [0076]    When it is assumed that the noise signal vector ({right arrow over (N)}(k)) and the audio signal vector ({right arrow over (B)}(k)) of the far-end talker signal are statistically independent from one another and a normal distribution has an average of 0, the probability that the acoustic echo signal vector ({right arrow over (Y)}(k)) will exist in the microphone input signal vector ({right arrow over (D)}(k)) may be obtained as expressed by Equation 24 below. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                        
                       
                         ( 
                         
                           
                             H 
                             1 
                           
                            
                           
                             
                               D 
                               → 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         P 
                          
                         
                           ( 
                           
                             
                               H 
                               1 
                               ′ 
                             
                              
                             
                               
                                 X 
                                 → 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                       = 
                       
                         1 
                         
                           1 
                           + 
                           
                             
                               
                                 p 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     1 
                                     ′ 
                                   
                                   ) 
                                 
                               
                               
                                 p 
                                  
                                 
                                   ( 
                                   
                                     H 
                                     0 
                                     ′ 
                                   
                                   ) 
                                 
                               
                             
                              
                             
                               
                                 ∏ 
                                 
                                   m 
                                   = 
                                   1 
                                 
                                 N 
                               
                                
                               
                                   
                               
                                
                               
                                 
                                   P 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           X 
                                           m 
                                         
                                          
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                        
                                       
                                         H 
                                         1 
                                         ′ 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   P 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           X 
                                           m 
                                         
                                          
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                        
                                       
                                         H 
                                         0 
                                         ′ 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     
                       P 
                        
                       
                         ( 
                         
                           
                             H 
                             0 
                           
                            
                           
                             
                               D 
                               → 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       1 
                       - 
                       
                         P 
                          
                         
                           ( 
                           
                             
                               H 
                               1 
                             
                              
                             
                               
                                 D 
                                 → 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     Here 
                     , 
                     
                       
 
                     
                      
                     
                       
                         ∏ 
                         
                           m 
                           = 
                           1 
                         
                         N 
                       
                        
                       
                           
                       
                        
                       
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 
                                   
                                     X 
                                     m 
                                   
                                    
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                  
                                 
                                   H 
                                   1 
                                   ′ 
                                 
                               
                               ) 
                             
                           
                           
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                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     24 
                   
                   ] 
                 
               
             
           
         
       
     
         [0077]    The sum (σ V     m     +S     m     2 (k)) of variances of the noise signal and the audio signal of the near-end talker signal required for obtaining the step size (μ m (k)) may be estimated by performing a smoothing operation with a factor (α) having a value 0&lt;α&lt;1 as expressed by Equation 25 below. 
         [0000]      σ V     m     +S     m     2 ( k+ 1)=ασ V     m     +S     m     2 ( k )+(1−α) E {(| V   m ( k )| 2   +|S   m ( k )| 2 )| D   m ( k )}
 
         [0000]      σ Y     m     2 ( k+ 1)=ασ Y     m     2 ( k )+(1−α) E {(| Y   m ( k )| 2 )| D   m ( k )}  [Equation 25]
 
         [0078]    Here, E{(|V m (k)| 2 +|S m (k)| 2 )|D m (k)} is expressed by Equation 26 below. Here, E{(|Y m (k)| 2 )|D m (k)} is expressed by Equation 27 below. 
         [0000]    
       
         
           
             
               
                 
                   
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                   [ 
                   
                     Equation 
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                      
                     26 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
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                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     27 
                   
                   ] 
                 
               
             
           
         
       
     
         [0000]    Equation 26 are expressed by Equation 28 below. 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
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                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     28 
                   
                   ] 
                 
               
             
           
         
       
     
         [0079]    Also, E{(|Y m (k)| 2 )|D m (k),H 0 } and E{(|Y m (k)| 2 )|D m (k),H 1 } in Equation 27 are expressed by Equation 29 below. 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         E 
                          
                         
                           { 
                           
                             
                               
                                 ( 
                                 
                                   
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                           } 
                         
                       
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                       0 
                     
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                       = 
                       
                         
                           
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                               1 
                               
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                                 + 
                                 
                                   
                                     
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                                       ^ 
                                     
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                            
                           
                             
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                                 Y 
                                 m 
                               
                               2 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             
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                                       ^ 
                                     
                                     m 
                                   
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                                     k 
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                                   1 
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                                         ξ 
                                         ^ 
                                       
                                       m 
                                     
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                                       ( 
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                                       ) 
                                     
                                   
                                 
                               
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                             2 
                           
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                                     m 
                                   
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                               2 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     29 
                   
                   ] 
                 
               
             
           
         
       
     
         [0080]    {circumflex over (ξ)}(k) in Equation 28 and Equation 29 is expressed by Equation 30 below. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ξ 
                         ^ 
                       
                       m 
                     
                      
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         σ 
                         
                           Y 
                           m 
                         
                         2 
                       
                        
                       
                         ( 
                         k 
                         ) 
                       
                     
                     
                       
                         σ 
                         
                           
                             V 
                             m 
                           
                           + 
                           
                             S 
                             m 
                           
                         
                         2 
                       
                        
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     30 
                   
                   ] 
                 
               
             
           
         
       
     
         [0081]    The foregoing Equation 25 to Equation 30 correspond to operations S 301  to S 325 . 
         [0082]    The present invention has been described on the assumption that the statistical model is a normal distribution, but the present invention may also be applicable to a Laplacian distribution, a gamma distribution, and the like, besides the normal distribution. 
         [0083]      FIG. 5  is a view illustrating a process of canceling acoustic echo by an acoustic echo canceller according to an embodiment of the present invention. The acoustic echo canceller cancels acoustic echo through the operations as described above with reference to  FIGS. 1 through 4 . 
         [0084]    The acoustic echo canceller estimates a variance (E{|E pri,m (k)| 2 }) of a residual signal, a variance (E{|V m (k)| 2 }) of a noise signal of a near-end talker signal, and a variance of an audio signal of the near-end talker signal (S 410 ). Operation S 410  corresponds to the variance estimation operation as described above with reference to  FIG. 4 . 
         [0085]    The acoustic echo canceller determines a step size (u(k)) (S 420 ). Operation S 420  corresponds to the step size determining operation as described above with reference to  FIG. 3 . 
         [0086]    The acoustic echo canceller updates an adaptive filter coefficient ({circumflex over ({right arrow over (W)}(k)) (S 430 ). Operation S 430  corresponds to the operation as described above with reference to  FIG. 2 . 
         [0087]    The acoustic echo canceller cancels an actual acoustic echo signal ({right arrow over (Y)}(k)) from a microphone input signal ({right arrow over (D)}(k)) by using an estimated acoustic echo signal ({circumflex over ({right arrow over (Y)}(k)) (S 440 ). Operation S 440  corresponds to the operation as described above with reference to  FIGS. 1 and 2 . 
         [0088]      FIG. 6  is a block diagram of an acoustic echo canceller  1000  according to an embodiment of the present invention. 
         [0089]    The acoustic echo canceller  1000  includes a variance estimating unit  1100 , a step size determining unit  1200 , an adaptive filter coefficient updating unit  1300 , and an acoustic echo cancelling unit  1400 . 
         [0090]    The variance estimating unit  1100  estimates a variance (E{|E pri,m (k)| 2 }) of a residual signal, a variance (E{|S m (k)| 2 }) of an audio signal of a near-end talker signal, and a variance (E{|V m (k)| 2 }) of a noise signal of the near-end talker signal. The variance estimating unit  1100  performs a variance estimating operation as described above with reference to  FIG. 4 . 
         [0091]    The step size determining unit  1200  determines a step size (u(k)) by using the variance (E{|E pri,m (k)| 2 }) of the residual signal, the variance (E{|S m (k)| 2 }) of the audio signal of the near-end talker signal, and the variance (E{|V m (k)| 2 }) of the noise signal of the near-end talker signal. The step size determining unit  1200  performs the step size determining operation as described above with reference to  FIG. 3 . 
         [0092]    The adaptive filter coefficient updating unit  1300  updates an adaptive filter coefficient ({circumflex over ({right arrow over (W)}(k)) by using the step size (u(k)). The adaptive filter coefficient updating unit  1300  performs the operation as described above with reference to  FIG. 2 . 
         [0093]    The acoustic echo cancelling unit  1400  cancels an actual acoustic echo signal ({right arrow over (Y)}(k)) from a microphone input signal ({right arrow over (D)}(k)) by using the estimated acoustic echo signal ({circumflex over ({right arrow over (Y)}(k)). Here, the estimated acoustic echo signal ({circumflex over ({right arrow over (Y)}((k)) is a signal obtained by estimating the actual acoustic echo signal ({right arrow over (Y)}(k)) by using the adaptive filter coefficient ({circumflex over ({right arrow over (W)}(k)). The acoustic echo cancelling unit  1400  performs the operation as described above with reference to  FIGS. 1 and 2 . 
         [0094]    According to embodiments of the present invention, a step size required for canceling acoustic echo is variably regulated by using a statistical model such that a post-residual signal is equal to a current near-end talker signal on the basis of an NLMS algorithm in a frequency domain. Accordingly, although an actual acoustic echo generation path (or RIR) is changed over time, an adaptive filter coefficient can be promptly adaptive to the actual acoustic echo generation path. Thus, according to an embodiment of the present invention, acoustic echo can be effectively canceled in an environment such as a mobile environment in which an actual acoustic echo generation path is frequently changed over time. 
         [0095]    Also, according to an embodiment of the present invention, on the basis of a statistical model resistant to noise changing over time, variances of an audio signal and a noise signal of a near-end talker signal and a variance of a residual signal can be more accurately estimated. Further, according to an embodiment of the present invention, since variances of an audio signal and a noise signal of a near-end talker signal and a variance of a residual signal are estimated in each frequency bin, an optimal step size can be obtained. 
         [0096]    In addition, according to an embodiment of the present invention, since a near-end talker signal is used in determining a step size, an additional effect of reducing a step size in a double-torque situation can be obtained. That is, according to an embodiment of the present invention, since a step size is reduced in a double-torque situation, an erroneous adaptive filter coefficient is not updated. Thus, since an erroneous adaptive filter coefficient is not updated, sound quality can be enhanced. 
         [0097]    While this invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.