Providing an introduction that is at once mathematical and intuitive, Random Signals and Noise allows readers to learn the theory through expository sections and examples. This book contains a chapter on spread spectrum techniques, a concise explanation of the physical origins of shot and thermal noise, an extensive explanation and use of the method of Lagrange multipliers, and a careful presentation of the Fourier transform. Assuming the reader has some background in calculus, it also offers reviews of probability and linear algebra. This textbook is intended for a first course in random signals and noise, includes examples, homework problems, case studies, and offers a solutions manual with qualifying course adoptions.
Zusammenfassung
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 FoundationBefore 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 ProblemsAlong with these traditional topics, the book includes a chapter devoted to spread spectrum techniques. It also demonstrates the use of MATLAB(R) 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.
Inhalt
Elementary Probability Theory. An Introduction to Stochastic Processes. The Weak Law of Large Numbers. The Central Limit Theorem. Extrema and the Method of Lagrange Multipliers. The Matched Filter for Stationary Noise. Fourier Series and Transforms. The Wiener-Khinchin Theorem and Applications. Spread Spectrum. More about the Autocorrelation and the PSD. Wiener Filters. Appendix: A Brief Overview of Linear Algebra. Bibliography. Index.