Abstract:
A feedback cancellation system with reduced sensitivity to low-frequency tonal inputs is provided. Such a system can be used, for example, in a hearing aid to prevent cancellation of the desired tonal inputs to the hearing aid, thus improving the gain at high frequencies of the hearing aid while simultaneously preserving the desired tonal inputs at low frequencies. The feedback cancellation system comprises a first adaptive filter block for adaptively filtering an error signal to remove the low-frequency tonal components from the error signal. The first adaptive filter block is constrained so that only low-frequency tones in the error signal are cancelled, thus enabling the feedback cancellation system to still cancel “whistling” at high frequencies due to the temporary instability of the hearing aid. A second adaptive filter block adaptively filters a feedback path signal to produce an adaptively filtered feedback path signal. The first and second adaptive filter blocks are identical and filter coefficients of the first adaptive filter block are copied to those of the second adaptive filter block. Using an LMS adaptation algorithm, filter coefficients of an adaptive filer of the feedback cancellation system are controlled by the adaptively filtered error signal and the adaptively filtered feedback path signal respectively inputted from the first and second adaptive filter blocks. The adaptive filter then produces an adaptively filtered modeled feedback signal to be subtracted from an electrical audio signal input for updating the error signal of the hearing aid. The hearing aid processes the updated error signal with a digital signal processor to generate an audio output.

Description:
CROSS-REFERENCES TO RELATED APPLICATION  
       [0001]    This application is a continuation-in-part of U.S. patent application Ser. No. 09/745,497, filed Dec. 21, 2000, which is incorporated in its entirety herein by reference for any and all purposes. 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    The present invention relates generally to apparatus and methods for adaptive feedback cancellation in an audio system such as a hearing aid and, more specifically, to a feedback cancellation system of the hearing aid with reduced sensitivity to low-frequency tonal inputs.  
         BACKGROUND OF THE INVENTION  
         [0003]    An audio system, such as a hearing aid, almost invariably incurs some sort of mechanical and/or acoustic feedback during operation of the audio system. The mechanical and/or acoustic feedback often limits the maximum gain that can be achieved in the hearing aid. Moreover, system instability caused by the feedback, whether mechanical and/or acoustic, is sometimes audible as a continuous high-frequency tone or whistle emanating from the hearing aid. The mechanical feedback of the hearing aid is usually caused by mechanical vibrations from a component thereof such as a receiver. Mechanical vibrations from the receiver of a high-power hearing aid can be reduced by combining outputs of two receiver units mounted back-to-back so as to cancel the net mechanical movement of the receiver units. As such, as much as 10 dB additional gain can be achieved for the high-power hearing aid before the onset of oscillation by the hearing aid. Many hearing aids also provide a venting capability to reduce unpleasant occlusion experienced by users of the hearing aids. But venting an earmold of a behind-the-ear (BTE) type hearing aid or a shell of an in-the-ear (ITE) type hearing aid establishes an acoustic feedback path that would limit the maximum possible gain to approximately less than 40 dB for a small vent and even less for a large vent. The acoustic feedback path includes effects from many of the hearing aid components such as the amplifier, receiver, and microphone as well as vent acoustics.  
           [0004]    As mentioned, the acoustic feedback of the hearing aid tends to cause system instability of the hearing aid, particularly at high frequencies. A traditional approach for increasing the stability of a hearing aid is to reduce the gain at high frequencies. Reducing the gain of the hearing aid only at high frequencies modifies the overall system frequency response of the hearing aid. Therefore, controlling feedback by modifying the system frequency response to avoid instability means that a desired high-frequency response of the hearing aid will be sacrificed. Phase shifters and notch filters have also been suggested to control feedback, but have not proven to be very effective.  
           [0005]    A more effective technique to control feedback is by feedback cancellation. For instance, an internal feedback signal is estimated and subtracted from a microphone signal of the hearing aid. Feedback cancellation typically uses an adaptive filter that models the dynamically changing feedback path of the hearing aid. Such an adaptive feedback cancellation system, however, can generate a large mismatch between an actual feedback path and an adaptive filter modeled feedback path when the input signal of the hearing aid is either narrowband or sinusoidal. One example of such a system has been disclosed by U.S. Pat. No. 5,091,952 to Williamson et al., as is illustrated in FIG. 1. FIG. 1 shows a hearing aid  100  having the adaptive feedback cancellation system incorporated therein. As shown in FIG. 1, an adaptive filter  101  is used to model the feedback path of the hearing aid, and a Least Mean Square (LMS) adaptation algorithm  103  is used to control filter coefficients adaptation of adaptive filter  101 . A delay  105  is placed in the feedback path model to decorrelate the hearing aid output from the input. The delay  105  improves the system convergence of the hearing aid for signals such as speech. However, for tonal inputs at low frequencies such as music, sinusoids, or audiological test signals commonly used to measure hearing loss of a patient, this system tends to cancel the tonal inputs instead of accurately modeling the actual feedback path of the hearing aid for feedback cancellation.  
           [0006]    An improved effective feedback cancellation scheme used in a hearing aid is disclosed by the present inventor in U.S. Pat. No. 6,072,884, entitled “Feedback Cancellation Apparatus and Methods”, the contents of which are incorporated herein by reference. This improved system is illustrated in FIG. 2. The feedback path of such improved system is modeled by the combination of an adaptive filter  201  and a delay  205  plus a slowly-varying or non-varying (frozen) filter  219 . The frozen filter  219  can be a frozen IIR filter or a frozen all pole filter, and the adaptive filter  201  can be an adaptive (all zero) FIR filter. Specifically, when the hearing aid is first turned on, filter (pole) coefficients of the frozen filter  219  are adapted to model those aspects of the feedback path that can have high-Q resonance but which stay relatively constant during normal hearing aid operation. Thus, pole coefficients of the feedback path, once determined, are modified and then frozen or, at least, changed vary slowly. Once the pole coefficients are determined, filter (zero) coefficients of the adaptive filter  201  are adapted to correspond to the modified poles. The objective of this adaptation is to minimize an error signal e(n) produced at the output of adder  209 . Unlike the filter coefficients of the frozen filter  219 , the adaptive filter  201  continues to adapt its filter coefficients in response to changes in the feedback path. Therefore, the adaptive filter  201  models those portions of the feedback path that are changing, and the frozen filter  219  models those portions of the feedback path that remain essentially constant while the hearing aid is in use. This improved system will, however, also attempt to cancel a tonal input signal. Nonetheless, adaptive filter coefficients of this improved system are constrained to prevent excessive deviation from an initial setting thereof. In the presence of a tonal input, the degree of input signal cancellation resulting from the adaptive filter is greatly reduced, but it is still not completely eliminated.  
           [0007]    The feedback cancellation systems shown in FIGS. 1 and 2 use the LMS algorithm for adaptation of the adaptive filter coefficients. As shown in FIGS. 1 and 2, the hearing aid receives an input signal x(n), a transfer function of a hearing aid processing unit is given by h(n), and the hearing aid output is y(n), where n is a sample index. The LMS algorithm adaptation in both the above-mentioned feedback cancellation systems uses the cross-correlation of an error signal e(n) and a feedback path signal d(n) that is inputted to the adaptive filter (i.e., the adaptive filter  101  or the adaptive filer  201 ). The objective of the adaptive filter is to minimize the power of the error signal e(n). Let the adaptive filter be a K-tap finite impulse response (FIR) filter having adaptive coefficients b l (n) through b k (n), a power-normalized adaptive filter update for input sample index n is then given by  
                 b   k          (     n   +   1     )       =         b   k          (   n   )       +     2        μ       σ   d   2          (   n   )              e        (   n   )            d        (     n   -   k     )                   (   1   )                               
 
           [0008]    where μ controls the rate of adaptation and σ d   2 (n) is the average power in the feedback path signal d(n). If the input signal x(n) is white noise, the adaptive filter will normally converge to a model of its feedback path. If the input x(n) is a pure tone, however, the adaptive feedback cancellation system will minimize the error signal e(n) by adjusting the filter coefficients b l (n) through b k (n) so that v(n), which is an adaptively filtered version of d(n), has the same amplitude and phase as of the input x(n) and thus will cancel the tone. Slowing the rate of adaptation by making μ smaller will reduce the tendency to cancel short-duration tonal inputs, but will also reduce the ability of the adaptive system to rapidly adapt to large changes to the acoustic feedback path.  
           [0009]    A further improvement in feedback cancellation for hearing aids is disclosed by Gao et al. in an international patent application WO 00/019605 A2. This system is illustrated in FIG. 3. As shown in FIG. 3, its feedback path is modeled by the combination of an adaptive filter  301 , a delay  305 , an LMS adaptation  303 , and a frozen filter  319 , as previously taught by the above-mentioned &#39;884 patent. In FIG. 3, however, both inputs to the LMS adaptation  303  used to update the adaptive filter coefficients are further filtered through fixed filters p(n)  321  and  323 . The fixed filters p(n)  321 ,  323  are bandpass or highpass filters, and emphasize a frequency region where mismatch between the actual and modeled feedback paths can cause the greatest stability problems in the hearing aid. Low frequencies, where the hearing aid typically has low gain but where tonal input signals are often experienced, are de-emphasized to minimize the possibility of canceling a tonal input. This further improved system relies on the fixed filters p(n)  321 ,  323  to reduce the potential mismatch when a tonal input is present, and the filter adaptation is not constrained.  
           [0010]    In the system of FIG. 3, the cancellation of tonal input signals is reduced by minimizing the power in a filtered version of the error signal instead of minimizing the broadband error. The inputs g(n) and f(n) to LMS adaptation  303  are passed through the respective fixed filters p(n)  321 ,  323  giving g(n)=e(n)*p(n) and f(n)=d(n)*p(n), where * denotes convolution by the fixed filters p(n)  321 ,  323 . The adaptive coefficient update for input sample n is then given by:  
                   b   k          (     n   +   1     )       =         b   k          (   n   )       +     2        μ       σ   f   2          (   n   )              g        (   n   )            f        (     n   -   k     )             ,           (   2   )                               
 
           [0011]    where μ controls the rate of adaptation and σ f   2 (n) is the average power in signal f(n). The use of a highpass filter for p(n), for example, is equivalent to making μ smaller at low frequencies, thus slowing the rate of adaptation for low-frequency input signals. However, even the system shown in FIG. 3 will tend to cancel a tonal input at low frequencies if the signal duration is long enough.  
           [0012]    A need, thus, remains in the art for apparatus and methods to reduce the cancellation of tonal input signals when implementing adaptive feedback cancellation in a hearing aid or other audio system.  
         SUMMARY OF THE INVENTION  
         [0013]    A feedback cancellation system with reduced sensitivity to low-frequency tonal inputs is provided. Such a system can be used, for example, in a hearing aid to prevent cancellation of the desired tonal inputs to the hearing aid, thus improving the gain at high frequencies while simultaneously preserving the desired tonal inputs at low frequencies. The feedback cancellation system comprises a first adaptive filter block for adaptively filtering an error signal to remove the low-frequency tonal components from the error signal. The first adaptive filter block is constrained so that only low-frequency tones in the error signal are cancelled, thus enabling the feedback cancellation system to still cancel “whistling” at high frequencies due to the temporary instability of the hearing aid. A second adaptive filter block adaptively filters the feedback path signal to produce an adaptively filtered feedback path signal. The first and second adaptive filter blocks are identical and filter coefficients of the first adaptive filter block are copied to those of the second adaptive filter block. Using an LMS adaptation algorithm, filter coefficients of the adaptive filer of the feedback cancellation system are controlled by the adaptively filtered error signal and the adaptively filtered feedback path signal respectively inputted from the first and second adaptive filter blocks. The adaptive filter then produces an adaptively filtered modeled feedback signal to be subtracted from an electrical audio signal input for updating the error signal of the hearing aid. The hearing aid processes the updated error signal with a digital signal processor to generate an audio output.  
           [0014]    Thus, in one aspect, the invention is an audio processing system such as used in a hearing aid, the audio processing system comprised of a signal path including a digital signal processing means for processing an error signal, and a feedback cancellation means that adaptively models an acoustic feedback path. The feedback cancellation means includes first adaptive filter means adaptively filtering the error signal to remove low-frequency tonal components of the error signal for coefficient adaptation of the acoustic feedback path model, an LMS adaptation means, and an adaptive filter. The filter coefficients of the adaptive filter are adaptively controlled by the adaptively filtered error signal to produced an adaptive feedback signal. Preferably, the signal path of the audio processing system is also comprised of an input transducer, a subtracting means, and an output transducer. In a preferred embodiment, the first adaptive filter means comprises at least one adaptive notch filter. If more than one adaptive notch filters are included in the first adaptive filter means, they are connected in cascade to each other. In another preferred embodiment, the first adaptive filter means comprises a fixed bandpass filter filtering the error signal and connected in cascade to the at least one adaptive notch filter. In yet another preferred embodiment, the first adaptive filter means comprises a fixed highpass filter filtering the error signal and connected in cascade to the at least one adaptive notch filter. In yet another preferred embodiment, the first adaptive filter means comprises a plurality of bandpass filters arranged in parallel combination and respectively receiving the error signal, a plurality of adaptive notch filters also arranged in parallel combination, and adder means for summing outputs of the plurality of adaptive notch filters. Each of the plurality of adaptive notch filters is connected to the output of one of the plurality of bandpass filters. In yet another preferred embodiment, the first adaptive filter means comprises a highpass filter filtering the error signal, a lowpass filter filtering the error signal, a delay delaying the output of the lowpass filter, an adaptive FIR filter adaptively filtering the output of the delay, a first subtracting means for subtracting the output of the adaptive FIR filter from the output of the lowpass filter, and a first adder means for summing the output of the first subtracting means and the output of the highpass filter.  
           [0015]    In another aspect, the invention is an audio processing system such as used in a hearing aid, the audio processing system comprised of a signal path including a digital signal processing means for processing an error signal, and a feedback cancellation means that adaptively models an acoustic feedback path. The feedback cancellation means includes first adaptive filter means adaptively filtering the error signal to remove low-frequency tonal components of the error signal for coefficient adaptation of the acoustic feedback path model, second adaptive filter means for adaptive filtering a feedback path signal, an LMS adaptation means, and an adaptive filter. The filter coefficients of the adaptive filter are adaptively controlled by the adaptively filtered error signal and by the adaptively filtered feedback path signal to produced an adaptive feedback signal. The first and second adaptive filter means are identical and filter coefficients of first adaptive filter means are copied to those of the second adaptive filter means. Preferably, the signal path of the audio processing system is also comprised of an input transducer, a subtracting means, and an output transducer. In a preferred embodiment, the first adaptive filter means comprises at least one adaptive notch filter. If more than one adaptive notch filters are included in the adaptive filter means, they are connected in cascade to each other. In another preferred embodiment, the first adaptive filter means comprises a fixed bandpass filter filtering the error signal and connected in cascade to the at least one adaptive notch filter. In yet another preferred embodiment, the first adaptive filter means comprises a fixed highpass filter filtering the error signal and connected in cascade to the at least one adaptive notch filter. In yet another preferred embodiment, the first adaptive filter means comprises a plurality of bandpass filters arranged in parallel combination and respectively receiving the error signal, a plurality of adaptive notch filters also arranged in parallel combination, and adder means for summing outputs of the plurality of adaptive notch filters. Each of the plurality of adaptive notch filters is connected to the output of one of the plurality of bandpass filters. In yet another preferred embodiment, the first adaptive filter means comprises a highpass filter filtering the error signal, a lowpass filter filtering the error signal, a delay delaying the output of the lowpass filter, an adaptive FIR filter adaptively filtering the output of the delay, a first subtracting means for subtracting the output of the adaptive FIR filter from the output of the lowpass filter, and a first adder means for summing the output of the first subtracting means and the output of the highpass filter.  
           [0016]    In yet another aspect, the invention is a method of feedback cancellation, such as used in a hearing aid, the method comprising the steps of receiving an input signal, generating an electrical audio signal in accordance with the input signal, processing the electrical audio signal by a digital signal processor to produce an electrical output signal, estimating an internal feedback signal in accordance with the electrical output signal, generating an error signal by subtracting the internal feedback signal from the electrical audio signal, adaptively filtering the error signal to remove low-frequency tonal components of the error signal with a first adaptive filter block, adaptively controlling filter coefficients of an adaptive filter in accordance with the adaptively filtered error signal, updating the internal feedback signal by the adaptive filter, updating the error signal by subtracting the updated internal feedback signal from the electrical audio signal, and processing the updated error signal by the digital signal processor to update the electrical output signal. In a preferred embodiment, the step of adaptively filtering the error signal is accomplished by filtering the error signal with at least one adaptive notch filter of the first adaptive filter block. In another embodiment, the step of adaptively filtering the error signal is accomplished by filtering the error signal with a bandpass filter and then with the at least one adaptive notch filter. In yet another embodiment, the step of adaptively filtering the error signal is accomplished by filtering the error signal with a highpass filter and then with the at least one adaptive notch filter. In yet another embodiment, the step of adaptively filtering the error signal comprises the steps of filtering the error signal with a plurality of bandpass filters arranged in parallel combination, filtering outputs of the plurality of bandpass filters with a plurality of adaptive notch filters also arrange in parallel combination, and generating the adaptively filtered error signal by summing outputs of the plurality of adaptive notch filters. In yet another embodiment, the step of adaptively filtering the error signal comprises the steps of generating a highpass error signal by filtering the error signal with a highpass filter, generating a lowpass filtered error signal by filtering the error signal with a lowpass filter, delaying the lowpass filtered error signal, generating an adaptively filtered lowpass error signal by filtering the delayed lowpass filtered error signal with an adaptive FIR filter, generating a lowpass error signal by subtracting the adaptively filtered lowpass error signal from the lowpass filtered error signal, and generating the adaptively filtered error signal by summing the lowpass error signal and the highpass error signal.  
           [0017]    In yet another aspect, the invention is a method of feedback cancellation, such as used in a hearing aid, the method comprising the steps of receiving an input signal, generating an electrical audio signal in accordance with the input signal, processing the electrical audio signal by a digital signal processor to produce an electrical output signal, estimating an internal feedback signal in accordance with the electrical output signal, generating an error signal by subtracting the internal feedback signal from the electrical audio signal, adaptively filtering the error signal to remove low-frequency tonal components of the error signal with a first adaptive filter block, delaying the electrical output signal with a delay unit, generating a feedback path signal by filtering an output of the delay unit with a frozen filter, generating an adaptive feedback path signal by filtering the feedback path signal with a second adaptive filter block, adaptively controlling filter coefficients of an adaptive filter in accordance with the adaptively filtered error signal and the adaptively filtered feedback path signal, updating the internal feedback signal by the adaptive filter, updating the error signal by subtracting the updated internal feedback signal from the electrical audio signal, and processing the updated error signal by the digital signal processor to update the electrical output signal. In a preferred embodiment, the step of adaptively filtering the error signal is accomplished by filtering the error signal with at least one adaptive notch filter of the first adaptive filter block. In another embodiment, the step of adaptively filtering the error signal is accomplished by filtering the error signal with a bandpass filter and then with the at least one adaptive notch filter. In yet another embodiment, the step of adaptively filtering the error signal is accomplished by filtering the error signal with a highpass filter and then with the at least one adaptive notch filter. In yet another embodiment, the step of adaptively filtering the error signal comprises the steps of filtering the error signal with a plurality of bandpass filters arranged in parallel combination, filtering outputs of the plurality of bandpass filters with a plurality of adaptive notch filters also arrange in parallel combination, and generating the adaptively filtered error signal by summing outputs of the plurality of adaptive notch filters. In yet another embodiment, the step of adaptively filtering the error signal comprises the steps of generating a highpass error signal by filtering the error signal with a highpass filter, generating a lowpass filtered error signal by filtering the error signal with a lowpass filter, delaying the lowpass filtered error signal, generating an adaptively filtered lowpass error signal by filtering the delayed lowpass filtered error signal with an adaptive FIR filter, generating a lowpass error signal by subtracting the adaptively filtered lowpass error signal from the lowpass filtered error signal, and generating the adaptively filtered error signal by summing the lowpass error signal and the highpass error signal.  
           [0018]    A further understanding of the nature and advantages of the present invention may be realized by reference to the remaining portions of the specification and the drawings. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0019]    [0019]FIG. 1 illustrates a hearing aid having an adaptive feedback cancellation system according to the prior art;  
         [0020]    [0020]FIG. 2 illustrates a hearing aid having an improved feedback cancellation scheme according to a second prior art;  
         [0021]    [0021]FIG. 3 illustrates yet another improved feedback cancellation scheme of a hearing aid according to a third prior art;  
         [0022]    [0022]FIG. 4 illustrates a hearing aid with a feedback cancellation system according to the present invention;  
         [0023]    [0023]FIG. 5 illustrates a signal flow chart of the adaptation of the feedback model;  
         [0024]    [0024]FIG. 6 illustrates a cascade of adaptive notch filters used in the adaptive filter block p(n) shown in FIG. 4;  
         [0025]    [0025]FIG. 7 illustrates a cascade of a fixed filter with adaptive notch filters used in the adaptive filter block p(n) shown in FIG. 4;  
         [0026]    [0026]FIG. 8 illustrates a parallel combination of constrained notch filters used in the adaptive filter block p(n) shown in FIG. 4; and  
         [0027]    [0027]FIG. 9 illustrates an adaptive line enhancer in the adaptive filter block p(n) shown in FIG. 4. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0028]    [0028]FIG. 4 shows a simplified block diagram of hearing aid  400  according to a preferred embodiment of the present invention. It is also understood that the feedback cancellation system of the present invention can be used in other applications, such as audio systems, audio broadcasting systems, telephony, and the like. It should also be understood that hearing aid  400  can be an in-the-canal, in-the-ear, behind-the-ear, or otherwise mounted hearing aid.  
         [0029]    The hearing aid  400  includes microphone  407  for receiving an input signal x(n), and a feedback signal via acoustic feedback path  417  of the hearing aid, to produce an electrical audio signal s(n), where n is a sample index. An adaptively filtered feedback signal v(n) outputted from adaptive filter  401  is subtracted from the electrical audio signal s(n) by adder  409  to produce an error signal e(n). The error signal e(n) is inputted into hearing aid processing unit  411 , which is a digital signal processor, to generate electrical output  425 . The electrical output  425  of hearing aid processing unit  411  is amplified by amplifier  413  and then converted into an audio output y(n) by receiver  415 . The audio output y(n) is fed back to microphone  407  via acoustic feedback path  417 .  
         [0030]    The electrical output  425  of hearing aid processing unit  411  is shifted in time by delay  405  and then filtered by frozen filter  419  to generate a feedback path signal d(n). The frozen filter  419  is a slowing-varying or non-varying (frozen) filter. The feedback path signal d(n) from the frozen filter  419  is inputted into adaptive filter  401  for generating the adaptively filtered feedback signal v(n). The frozen filter  419  can be a frozen all-pole filter or a frozen IIR filter, and the adaptive filter  401  can be an adaptive (all-zero) FIR filter. Specifically, when the hearing aid  400  is first turned on, filter (pole) coefficients of the frozen filter  419  are adapted to model those aspects of the feedback path that can have high-Q resonance but which stay relatively constant during normal hearing aid operation. Thus, pole coefficients of the feedback path, once determined, are modified and then frozen or, at least, changed vary slowly. Once the pole coefficients are determined, filter (zero) coefficients of the adaptive filter  401  are adapted to correspond to the modified poles. The objective of this adaptation is to minimize the error signal e(n) produced at the output of adder  409 . Unlike the filter coefficients of the frozen filter  419 , the adaptive filter  401  continues to adapt its filter coefficients in response to changes in the feedback path. Therefore, the adaptive filter  401  models those portions of the feedback path that are changing, and the frozen filter  419  models those portions of the feedback path that remain essentially constant while the hearing aid is in use.  
         [0031]    The hearing aid  400  further includes first and second adaptive filter blocks p(n)  421 ,  423 , as compared to fixed filters p(n)  321 ,  323  of the prior art shown in FIG. 3. The first adaptive filter block p(n)  421  adapts to minimize the power of the error signal e(n) by generating a filtered error signal g(n) at its output. In the preferred embodiment of the present invention, the filtered error signal g(n) forms a first input to Least Mean Square (LMS) adaptation  403  of the feedback path model. In other embodiments, the LMS adaptation  403  may be replaced by other suitable adaptation algorithms. For instance, more sophisticated adaptation algorithms may offer faster convergence to the hearing aid. Such algorithms, however, generally require much greater amounts of computation and therefore may not be as practical for a hearing aid. Filter coefficients of first adaptive filter block p(n)  421  are copied to second adaptive filter block p(n)  423 , which modifies the feedback path signal d(n) to produce filtered feedback path signal f(n) as a second input to LMS adaptation  403 . The second adaptive filter block p(n)  423  is identical to the first adaptive filter block p(n)  421 . The LMS adaptation  403  controls adaptation of the filter coefficients of adaptive filter  401 .  
         [0032]    A simplified signal flow chart of a feedback model adaptation according to the present invention is illustrated in FIG. 5. As shown in FIG. 5, the hearing aid  400  in step  501  generates the error signal e(n) using a Microphone-Feedback Path model. In step  503 , the error signal e(n) is inputted into a first frequency select filter, which is the first adaptive filter block p(n)  421  shown in FIG. 4, to generate the filtered error signal g(n). In step  507 , the filtered error signal g(n) is sensed and analyzed and the filter coefficients of the first frequency select filter are updated to minimize the power of the filtered error signal g(n). The filter coefficients of the first frequency select filter are copied to a second frequency select filter, which is the second adaptive filter block p(n)  423 , in step  505 .  
         [0033]    In step  513 , hearing aid processing unit  411  processes the error signal e(n) to generate electrical output  425 , which is then tapped by delay  405  and filtered by frozen filter  419  to generate the feedback path signal d(n). The feedback path signal d(n) is filtered in step  515  by the second frequency select filter to generate filtered feedback path signal f(n). As mentioned, the filter coefficients of the second frequency select filter are copied and updated from the first frequency select filter during step  505 . Subsequently, in step  509 , the g(n) and the f(n) are cross-correlated by LMS adaptation  403 . The LMS adaptation  403  then generates adaptive model coefficient update for adaptively updating the filter coefficients of adaptive filter  401  in step  511 .  
         [0034]    There are several ways in which the first and second adaptive filter blocks p(n)  421 ,  423  can be designed, as shown in FIGS.  6 - 9 . FIG. 6 illustrates a preferred embodiment of the first adaptive filter block p(n)  421  or the second adaptive filter block p(n)  423  according to the present invention. As shown in FIG. 6, the first adaptive filter block p(n)  421  includes a cascade of adaptive digital notch filters  601  connected in series to each other. Although FIG. 6 indicates that three or more adaptive digital notch filters  601  are included in the adaptive filter block p(n), as few as only one adaptive digital notch filter  601  can be sufficient for the first and second adaptive filter blocks p(n)  421 ,  423 . A digital notch filter  601  is generally given by the transfer function  
               N        (   z   )       =       1   -     2      r                 cos                   (     ω   o     )          z     -   1         +       r   2          z     -   2             1   -     2      ρ                 r                 cos                   (     ω   o     )          z     -   1         +         (     ρ                 r     )     2          z     -   2                     (   3   )                               
 
         [0035]    where r is the pole radius, ω o  is the notch center frequency in radians, and ρ controls the notch width of the digital notch filter  601 . According to the preferred embodiment, parameter values found to be effective in practice for the preferred embodiment are r=0.99, ρ=0.5, and a constraint applied to limit 0≦ω o ≦π/4 for a system having a 16-kHz digital sampling rate. Other parameter values can also be used under different conditions or considerations. In general, the adaptive digital notch filter  601  can be designed by setting r and ρ to pre-selected values of less than 1, and adapting the remaining parameter cos(ω o ) to control a notch center frequency of the adaptive digital notch filter  601 . More preferably, the pole radius r is set to within the range of 0.5≦r≦1 and the value of ρ is set to within the range of 0.3≦ρ≦0.7.  
         [0036]    If we let c(n)≡cos(ω o ) for sample index n, and define e(n) as an input to the adaptive notch filter  601  and g(n) as the output, then the adaptive notch filter  601  is given by:  
                     u        (   n   )       =                  e        (   n   )       +     2      ρ                 rc                   (   n   )          u        (     n   -   1     )         -         (     ρ                 r     )     2          u        (     n   -   2     )                         g        (   n   )       =                  u        (   n   )       -     2                   rc        (   n   )            u        (     n   -   1     )         +       r   2          u        (     n   -   2     )                         c        (     n   +   1     )       =                  c        (   n   )       +     2      μ                   rg        (   n   )            u        (     n   -   1     )                         (   4   )                               
 
         [0037]    where u(n) is an output from filtering with just the pole pair, g(n) is the result of then filtering with the zero pair, and μ controls the rate of adaptation of the notch center frequency. Typically, the notch center frequency is constrained so that 0.707≦c(n)≦1. The adaptive notch filter  601  cancels low frequency tones in the error signal e(n), and the constraint on c(n) ensures that the adaptive feedback cancellation system of the hearing aid  400  cancels only low-frequency tonal components of the error signal e(n). High-frequency tones are not canceled, so the feedback cancellation system will still remove “whistling” caused by momentary instability in hearing aid  400 . Furthermore, the ability of the presently described feedback cancellation system to adjust to changes in the feedback path at high frequencies is not affected by the adaptive notch filter  601  due to the constraint on the center frequency thereof. More than one adaptive notch filter  601  can be used in series, with each notch filter  601  tending to cancel a different sinusoid in the error signal e(n).  
         [0038]    [0038]FIG. 7 shows another preferred embodiment of the first adaptive filter block p(n)  421  or the second adaptive filter block p(n)  423 . In FIG. 7, one or more identical adaptive notch filters  703  are combined in cascade with fixed initial filter  701 . Similar to the embodiment shown in FIG. 6, as few as only one adaptive notch filter  703  can be sufficient for the first and second adaptive filter blocks p(n)  421 ,  423 . For the first adaptive filter block p(n)  421 , the fixed initial filter  701  is inputted with the error signal e(n). Moreover, the fixed initial filter  701  can be a bandpass or highpass filter. The fixed initial filter  701  removes much of the low-frequency power in the error signal e(n), thereby reducing the possibility of feedback cancellation artifacts caused by a low frequency tonal input such as speech or music. The adaptive notch filter  703  then removes any remaining low-frequency sinusoids, thus further reducing the occurrence of processing artifacts. Like the adaptive notch filter  601  shown in FIG. 6, the adaptive notch filter  701  has constraint on its notch filter center frequency. Again, the constraint on the notch filter center frequency allows the feedback cancellation system to adjust to any changes in the feedback path that occur at high frequencies.  
         [0039]    [0039]FIG. 8 shows yet another preferred embodiment of the first adaptive filter block p(n)  421  or the second adaptive filter block p(n)  423  according to the present invention. As shown in FIG. 8, the error signal e(n) is inputted into a parallel combination of K fixed bandpass filters  801 ,  803 , . . .  805 , where K is the number of the bandpass filters. Each fixed bandpass filter independently operates to pass a specific frequency band of the error signal e(n). An output of each of the K fixed bandpass filters  801 ,  803 , . . .  805  is coupled to a corresponding adaptive notch filter  807 , respectively. Accordingly, each adaptive notch filter  807  is constrained to operate in a separate frequency region, and adapts to minimize the error signal power in that frequency band. The adaptation of each adaptive notch filter  807  is independent, and the notch depth and bandwidth can be adjusted to optimize the performance of the ensemble of filters. The filtered error signal g(n) is then the sum of output signals filtered by the notch filters  807  in all frequency bands.  
         [0040]    [0040]FIG. 9 shows yet another preferred embodiment of the first adaptive filter block p(n)  421  or the second adaptive filter block p(n)  423 . As shown in FIG. 9, adaptive FIR filter  907  is used to cancel low frequency tones instead of using an adaptive notch filter. In another embodiment, an IIR filter can be used as the adaptive filter  907 . A pair of initial filters is used to separate frequency ranges of the error signal e(n) received by the adaptive filter block p(n)  421  or  423 . In FIG. 9, lowpass filter  903  and highpass filter  901  receive the error signal e(n) at their inputs and produce lowpass and highpass filtered error signals t(n) and q(n) at their outputs, respectively. The lowpass filtered error signal t(n) is shifted in time by delay  905  and then is filtered by adaptive FIR filter  907  to produce adaptively filtered error signal w(n). The adaptively filtered error signal w(n) is subtracted from the lowpass filtered error signal t(n) by adder  911 , and the output of adder  911  is then added to the highpass filtered error signal q(n) to generate the filtered error signal g(n) of the adaptive filter block p(n)  421  or  423 . The high frequencies in the error signal e(n) are not modified, thus allowing the feedback cancellation system to adapt to changes in the feedback path at high frequencies. However, tonal components are removed from the low-frequency portion of the lowpass filtered error signal t(n) due to delay  905  and adaptive FIR filter  907 . As a result, the adaptive filter block p(n)  421  or  423  is controlled by a difference signal t(n)-w(n), and the adaptation minimizes the power in this difference signal. Because delay  905  decorrelates the low-frequency error signal w(n) passed through adaptive FIR filter  907  with respect to the low-frequency error signal t(n) that is not filtered by adaptive FIR filter  907 , the adaptive FIR filter  907  will not cancel low-frequency noises or random inputs. Tones in the low-frequency error signal t(n) remain correlated with the error signal w(n) despite the delay, however, so the first adaptive filter block p(n)  421  will cause the cancellation of tonal portions of a low-frequency signal. Such result is a system that cancels low-frequency tonal components of an error signal while leaving the high-frequency portion of the error signal unmodified. Since the low-frequency tonal components of the error signal e(n) are removed prior to the LMS adaptation of filter coefficients of the adaptive filter  401 , the adaptively filtered feedback signal v(n) generated by the adaptive filter  401  contains no low-frequency tonal components of the input signal. Therefore, when the adaptively filtered feedback signal v(n) is subtracted from the electrical audio signal s(n) by adder  409  to generate the error signal e(n), the tonal components of the electrical audio signal s(n) will not be cancelled and the low-frequency response of the hearing aid  400  will not be sacrificed. The system illustrated in FIG. 9 will typically require a much greater amount of computation than those of FIGS.  6 - 8 , so the embodiments given by FIGS.  6 - 8  are often preferred in practice. However, the system illustrated in FIG. 9 generally would generate a more accurate result as compared to those systems illustrated in FIGS.  6 - 8  in canceling the low-frequency tonal components of an error signal while leaving the high-frequency portion of the error signal unmodified. Moreover, since the system illustrated in FIG. 9 will not cancel low-frequency noises or random inputs, these low frequency noises or random inputs are included in the adaptively filtered feedback signal v(n). As a result, the low frequency noises and/or the random inputs may be removed from the error signal e(n) due to the system illustrated in FIG. 9.  
         [0041]    As will be understood by those familiar with the art, the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. Accordingly, the disclosures and descriptions herein are intended only to be illustrative, but not limiting, of the scope of the invention which is set forth in the following claims.