Random Processes: Filtering, Estimation, and Detection

PREFACE

Every day we are confronted with signals that we cannot model exactly by an analytical expression or in a deterministic manner. Examples of such signals are ordinary speech waveforms, selections of music, seismological signals, biological signals, passive sonar records, temperature histories, and communication signals. Signals representing the same spoken word by a number of people or by the same person at different times will have similarities and differences that we can’t seem to handle with deterministic modeling. How do we model them? Such signals can be described as somehow random and can be mathematically characterized as random processes. The characterization takes on a different form than an analytical expression and has several levels of sophistication where precise statements about the signals as a collection can be made only in a probabilistic sense. For example, we could say that at a given time the probability that a given random process is greater than a certain value is 0.25.

Random processes are basic in the fields of electrical and computer engineering—especially in the communication theory, computer vision, and digital signal processing areas—as well as vibrational theory and stress analysis in mechanical engineering. The digital processing of random signals is critical to high-performance communication systems, and nonlinear signal processing is consistently used to perform this processing.

These random processes serve as inputs to deterministic linear ...