ABSTRACT

Understanding the nature of random signals and noise is critically important for detecting signals and for reducing and minimizing the effects of noise in applications such as communications and control systems. Outlining a variety of techniques and explaining when and how to use them, Random Signals and Noise: A Mathematical Introduction focuses on applications and practical problem solving rather than probability theory.

A Firm Foundation
Before launching into the particulars of random signals and noise, the author outlines the elements of probability that are used throughout the book and includes an appendix on the relevant aspects of linear algebra. He offers a careful treatment of Lagrange multipliers and the Fourier transform, as well as the basics of stochastic processes, estimation, matched filtering, the Wiener-Khinchin theorem and its applications, the Schottky and Nyquist formulas, and physical sources of noise.

Practical Tools for Modern Problems
Along with these traditional topics, the book includes a chapter devoted to spread spectrum techniques. It also demonstrates the use of MATLAB® for solving complicated problems in a short amount of time while still building a sound knowledge of the underlying principles.

A self-contained primer for solving real problems, Random Signals and Noise presents a complete set of tools and offers guidance on their effective application.

chapter 1|30 pages

Elementary Probability Theory

chapter 2|10 pages

An Introduction to Stochastic Processes

chapter 3|14 pages

The Weak Law of Large Numbers

chapter 4|18 pages

The Central Limit Theorem

chapter 6|16 pages

The Matched Filter for Stationary Noise

chapter 7|20 pages

Fourier Series and Transforms

chapter 9|16 pages

Spread Spectrum

chapter 10|6 pages

More about the Autocorrelation and the PSD

chapter 11|14 pages

Wiener Filters