Algorithms for Communications Systems and their Applications, 2nd Edition

Chapter 3Adaptive transversal filters

We reconsider the Wiener filter introduced in Section 2.1. Given two random processes and , we want to determine the coefficients of a finite impulse response (FIR) filter having input , so that its output is a replica as accurate as possible of the process . Adopting, for example, the mean‐square error (MSE) criterion, the knowledge of the autocorrelation matrix of the filter input vector and the crosscorrelation between the desired output and the input vector are required. Next, the filter coefficients are determined by solving the system of equations (2.27). When the autocorrelation and crosscorrelation are not known a priori, but only (long) realizations of and are available, two approaches are possible. The direct approach provides that both ...