Adaptive Filtering: Algorithms and Practical Implementation by Paulo Sergio Ramirez DINIZ (auth.)

By Paulo Sergio Ramirez DINIZ (auth.)

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S. Haykin, Adaptive Filter Theory, Prentice Hall, Englewood Cliffs, NJ, 4th edition, 2002. 18. L. R. Rabiner and R. W. Schaffer, Digital Processing Prentice Hall, Englewood Cliffs, NJ, 1978. 0/ Speech Signals, 19. D. H. Johnson and D. E. Dudgeon, Array Signal Processing, Prentice Hall, Englewood Cliffs, NJ, 1993. 20. T. Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, NJ, 1980. 21. D. G. Luenberger, Introduction to Linear and Nonlinear Programming, Addison Wesley, Reading, MA, 1973. 1 INTRODUCTION This chapter includes a brief review of deterministic and random signal representations.

In Fig. 1. 7 is shown the input signal. The coefficients of the adaptive filter are adjusted in order to keep the squared value of the output error as small as possible. As can be noticed in Fig. 8, as the number of iterations increase the error signal resembles the discrete-time tri angular waveform shown in the same figure (dashed curve). 6 60 hemlions. k 80 Desired signal. 8 40 60 heralions. k 80 100 120 Error signal and triangular waveform. References 1. P. S. R. Diniz, E. A. B. da Silva, and S.

Although both methods are not directly applicable to practical adaptive filtering, smart reflections inspired on them led to practical algorithms such as the least-mean-square (LMS) [3]-[4] and Newton-based algorithms. The Newton and steepest-descent algorithms are introduced in this chapter, whereas the LMS algorithm is treated in the next chapter. Also, in the present chapter, the main applications of adaptive filters are revisited and discussed in greater detail. 2 SIGNAL REPRESENTATION In this section, we briefly review so me concepts related to deterministic and random discrete-time signals.

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