Algorithms for Communications Systems and their Applications, 2nd Edition

Chapter 2The Wiener filter

The theory of the Wiener filter [1, 2] that will be presented in this chapter is fundamental for the comprehension of several important applications. The development of this theory assumes the knowledge of the correlation functions of the relevant processes. An approximation of the Wiener filter can be obtained by the least squares (LS) method, through realizations of the processes involved.

The section on estimation extends the Wiener filter to a structure with multiple inputs and outputs. Next, some examples of application of the developed theory are illustrated.

2.1 The Wiener filter

With reference to Figure 2.1, let and be two individually and jointly wide sense stationary (WSS) random processes with zero mean; the problem is to determine the finite impulse system (FIR) filter so that, if the filter input is , the output replicates as closely as possible , for each . The Wiener theory provides the means to design the required filter.

Figure 2.1 ...