7.1 INTRODUCTION

In Chapter 6, we developed techniques for estimating random and nonrandom parameters. We also studied measures to determine the "goodness" of the estimates. In many applications, the goal was to estimate a signal waveform from a noisy version of the signal in an "optimal" manner.

In this chapter, we assume that the received signal is corrupted by an additive noise. We would like to extract the desired signal from the received signal based on the linear minimum mean-square error criterion. The received process signal, Y( t), is observed over some interval of time t ?[ t _i, t _f], where t _i, denotes initial time and t _f denotes final time. The problem is to determine ?( t), a linear estimate of Y( t). When t is outside the interval, we talk about prediction. If t < t _i, then ?( t) is a backward predictor. If t > t _f, then ?( t) is a forward predictor. When t ?[ t _i, t _f], the problem is referred to as smoothing. The process of extracting the information-carrying signal S(t) from the observed signal Y( t), where Y( t) = S( t) + N( t) and N( t) is a noise process, is called filtering. In Section 7.2,...