Applied Digital Signal Processing Theory and Practice

To use stochastic process models in practical signal processing applications, we need to estimate their parameters from data. In the first part of this chapter we introduce some basic concepts and techniques from estimation theory and then we use them to estimate the mean, variance, ACRS, and PSD of a stationary random process model. In the second part, we discuss the design of optimum filters for detection of signals with known shape in the presence of additive noise (matched filters), optimum filters for estimation of signals corrupted by additive noise (Wiener filters), and finite memory linear predictors for signal modeling and spectral estimation applications. We conclude with a discussion of the Karhunen–Loève transform, which is an optimum finite orthogonal transform for representation of random signals.

Study objectives

After studying this chapter you should be able to:

• Compute estimates of the mean, variance, and covariance of random variables from a finite number of observations (data) and assess their quality based on the bias and variance of the estimators used.

• Estimate the mean, variance, ACRS sequence, and PSD function of a stationary process from a finite data set by properly choosing the estimator parameters to achieve the desired quality in terms of bias–variance trade-offs.

• Design FIR matched filters for detection of known signals corrupted by additive random noise, FIR Wiener filters that minimize the mean squared error between the output signal and a desired response, and finite memory linear predictors that minimize the mean squared prediction error.

• […]