By Jacob Benesty, Yiteng Huang
By adaptive sign processing, we suggest, more often than not, adaptive ?ltering.In- recognized environments the place we have to version, determine, or tune time-varying channels, adaptive ?ltering has been confirmed to be an e?ective and robust device. for that reason, this instrument is now in use in lots of di?erent ?elds. because the invention, by means of Widrow and Ho? in 1959, of 1 of the ?rst advert- tive ?lters, the so-called least-mean-square, many purposes seemed to have the aptitude to take advantage of this primary notion. whereas the variety of - plications (using adaptive algorithms) has been (and retains) ?ourishing with time, due to a number of successes, the necessity for extra subtle adaptive algorithms turned seen as real-world difficulties are extra advanced and extra challenging. although the speculation of adaptive ?ltering is already a well-established subject in sign processing, new and greater innovations are stumbled on each year via researchers. a few of these fresh techniques are mentioned during this publication. The aim of this publication is to supply, for the ?rst time, a connection with the most well liked real-world purposes the place adaptive ?ltering recommendations play a massive function. to take action, we invited most sensible researchers in di?erent ?elds to c- tribute chapters addressing their speci?c subject of analysis. hundreds of thousands of pages wouldprobablynotbe enoughto describeallthe practicalapplicationsutil- ing adaptive algorithms. hence, we restricted the themes to a couple vital purposes in acoustics, speech, instant, and networking, the place examine continues to be very energetic and open.
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Additional info for Adaptive Signal Processing: Applications to Real-World Problems
3 Performance Metric A useful performance metric is the estimated maximum stable gain (MSG). 14) where H(ω) is the hearing aid gain, W (ω) is the feedback path model, and F (ω) is the actual feedback path response. 10) with z −1 = e−jω . The maximum stable hearing aid gain as a function of frequency is then |H(ω)| < 1 . 15) The maximum stable gain (MSG) is the maximum allowable gain value assuming a ﬂat frequency response for the hearing aid: MSG = min ω 1 |W (ω) − F (ω)| . 16) 2 Adaptive Feedback Cancellation in Hearing Aids 37 The MSG is therefore determined by the frequency at which the mismatch between the feedback model and the actual feedback path is greatest.
But in the 2 Adaptive Feedback Cancellation in Hearing Aids 41 case of a sinusoid or tonal input, the new algorithm greatly reduces the occurrence of processing artifacts because the artifacts are generally the result of unconstrained growth in the magnitude of the adaptive ﬁlter coeﬃcients. Thus the adaptation with a cost function reduces coloration and improves system stability at the expense of a reduction in the ability to model large deviations from the initial feedback path. 3 Simulation Results A feedback-cancellation system using closed-loop adaptation without a probe signal was simulated in MATLAB.
Q(n) = a segment of white noise. t(n) = the noise sequence q(n) ﬁltered through the DC zero ﬁlter D(z) = 1 − z −1 . This high-pass ﬁltering is to duplicate the DC zero ﬁlter used in the running adaptation to remove the DC bias in the sampled data. z(n) = r(n) ∗ t(n), the ﬁltered noise convolved with the impulse response. The ARX procedure is used to ﬁnd the ﬁlter which, when convolved with t(n), produces the closest match to z(n). 8) 2 Adaptive Feedback Cancellation in Hearing Aids 35 where ma is the number of poles in the model, mb is the number of zero coeﬃcients (number of zeros plus 1), and is the estimated feedback path delay.