TAILIEUCHUNG - DSP A Khoa học máy tính quan điểm P10

Adaptation We have already learned about many different types of systems. We started with frequency selective filters and filters designed for their time-domain properties. Then we saw nonfilters that had capabilities that filters lack, such as PLLs that can lock onto desired frequency components. Next we saw how to match a filter to a prespecified signal in order to best detect that signal. We have even glimpsed higher-order signal processing systems that can differentiate between signals with identical power spectra | Digital Signal Processing A Computer Science Perspective Jonathan Y. Stein Copyright 2000 John Wiley Sons Inc. Print ISBN 0-471-29546-9 Online ISBN 0-471-20059-X 10 Adaptation We have already learned about many different types of systems. We started with frequency selective filters and filters designed for their time-domain properties. Then we saw nonfilters that had capabilities that filters lack such as PLLs that can lock onto desired frequency components. Next we saw how to match a filter to a prespecified signal in order to best detect that signal. We have even glimpsed higher-order signal processing systems that can differentiate between signals with identical power spectra. Yet all these systems are simple in the sense that their design characteristics are known ahead of time. Nothing we have studied so far can treat problems where we are constantly changing our minds as to what the system should do. In this chapter we briefly discuss adaptive filters that is filters that vary in time adapting their coefficients according to some reference. Of course the term adaptive filter is a misnomer since by definition filters must be time-invariant and thus cannot vary at all However we allow this shameful usage when the filter coefficients vary much more slowly than the input signal. You may think that these adaptive filters would be only needed on rare occasions but in practice they are extremely commonplace. In order to understand how and why they turn up we disregard our usual custom and present three applications before tackling the more general theory. These applications noise cancellation echo cancellation and equalization turn out to have a lot in common. After this motivation we can introduce the more general problem stressing the connection with the Wiener-Hopf equations. Direct solution of these equations is usually impossible and so we will learn how to iteratively approximate a solution using the Widrow-Hoff equations and the LMS algorithm. We then briefly

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