By Jacob Benesty, Yiteng Huang
By adaptive sign processing, we suggest, often, adaptive ?ltering.In- recognized environments the place we have to version, determine, or music time-varying channels, adaptive ?ltering has been confirmed to be an e?ective and robust device. for that reason, this software is now in use in lots of di?erent ?elds. because the invention, via 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 capability to exploit this basic notion. whereas the variety of - plications (using adaptive algorithms) has been (and retains) ?ourishing with time, because of numerous successes, the necessity for extra refined adaptive algorithms grew to become noticeable as real-world difficulties are extra advanced and extra hard. even supposing the idea of adaptive ?ltering is already a well-established subject in sign processing, new and more suitable options are found each year by means of researchers. a few of these contemporary ways are mentioned during this ebook. The target of this publication is to supply, for the ?rst time, a connection with the most popular real-world functions the place adaptive ?ltering strategies play a massive position. to take action, we invited best researchers in di?erent ?elds to c- tribute chapters addressing their speci?c subject of research. millions of pages wouldprobablynotbe enoughto describeallthe practicalapplicationsutil- ing adaptive algorithms. for this reason, we restricted the themes to a couple vital purposes in acoustics, speech, instant, and networking, the place learn remains to be very energetic and open.
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Additional resources for Adaptive Signal Processing: Applications to Real-World Problems
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. If no feedback cancellation is used, W (ω) = 0 and the MSG will be determined by the peak of the measured feedback path response F (ω).
1) Because C is a low-pass response and B is a high-pass response with reduced gain, one can safely assume that the product |B · C| 1. This assumption leads to a useful approximate solution: Q · A · R + X[C + H(W · C + M · A · R)] Y ∼ . 2) Thus the output consists of the probe signal (if used) ﬁltered by the ampliﬁer and receiver, plus the microphone input modiﬁed by the vent feed-forward path and the hearing-aid processing. 2) shows that the system will be stable if either the gain of the hearing-aid processing H is low or if the feedback cancellation ﬁlter W comes close to canceling the feedback path M · A · R · B.
Benesty and S. L. Gay, “An improved PNLMS algorithm,” in Proc. IEEE ICASSP, 2002. 10. R. K. Martin, W. A. Sethares, R. C. Williamson, and C. R. , “Exploiting sparsity in adaptive ﬁlters,” in Conference on Information Sciences and Systems, The John Hopkins University, 2001. 11. S. L. Gay and S. C. Douglas, “Normalized natural gradient adaptive ﬁltering for sparse and nonsparse systems,” in Proc. IEEE ICASSP, 2002. 12. Y. Huang and J. Benesty, “Adaptive multi-channel least mean square and Newton algorithms for blind channel identiﬁcation,” Signal Processing, vol.