6 - Statistical Signal Processing

Abstract

This chapter presents a brief introduction to basic concepts critical to statistical signal processing. Statistical signal processing is an important subject in signal processing that enjoys a wide range of applications, including communications, control systems, medical signal processing, and seismology. It plays an important role in the design, analysis, and implementation of adaptive filters, such as adaptive equalizers in digital communication systems. The fundamental problems of statistical signal processing are those of signal detection and estimation that aim to extract information from the received signals and help make decisions. The principles of Bayesian and Fisher statistics relevant to estimation are presented. In the discussion of Bayesian statistics, emphasis is placed on two types of estimators: the minimum mean-squared error (MMSE) estimator and the maximum a posteriori (MAP) estimator. An important class of linear estimators, namely the Wiener filter, is also presented as a linear MMSE estimator. In the discussion of Fisher statistics, emphasis is placed on the maximum likelihood estimator (MLE), the concept of sufficient statistics, and information inequality that can be used to measure the quality of an estimator. This chapter also includes a brief discussion of signal detection. The signal detection problem is presented as one of binary hypothesis testing. Both Bayesian and Neyman-Pearson optimum criteria are presented and shown to be implemented with likelihood ratio tests.