Introduction to Random Processes, With Applications to Signals & Systems, Second Edition
This text/reference book aims to present a comprehensive introduction to the theory of random processes with emphasis on its practical applications to signals and systems. The author shows how to analyze random processes - the signals and noise of a communication system. He also shows how to achieve results in their use and control by drawing on probabilistic concepts and the statistical theory of signal processing. This second edition adds over 50 worked exercises for students and professionals, as well as an additional 100 standard exercises. Recent advances in random process theory and application have been added.
Why Read This Book
You should read this book if you need a rigorous yet application-minded grounding in random process theory that directly supports work in DSP, communications, radar, and audio/speech systems. You will learn how to model, analyze, and manipulate stochastic signals and noise so you can design and evaluate filters, estimators, and spectral analysis methods used in real engineering systems.
Who Will Benefit
Graduate students and practicing engineers in signal processing, communications, radar, or audio who need a mathematically sound reference for applying random-process theory to real systems.
Level: Advanced — Prerequisites: Undergraduate-level probability and statistics, calculus, linear systems and signals (continuous- and discrete-time), and basic familiarity with Fourier transforms and linear algebra.
Key Takeaways
- Model random signals and noise using stationary, ergodic, and Gaussian process frameworks.
- Compute and interpret autocorrelation, cross-correlation, and power spectral density for continuous- and discrete-time processes.
- Design and analyze linear systems subject to stochastic inputs, including Wiener filtering and linear MMSE estimation.
- Apply spectral analysis and estimation techniques (periodogram, windowing, parametric methods) and relate them to FFT implementations.
- Formulate and evaluate statistical detection and estimation problems for communications and radar signals.
- Analyze adaptive filtering behavior and convergence using stochastic process and statistical methods.
Topics Covered
- 1. Review of Probability, Random Variables, and Statistical Concepts
- 2. Definition and Classification of Random Processes
- 3. Stationarity, Ergodicity, and Moments of Stochastic Processes
- 4. Autocorrelation, Cross-Correlation, and Power Spectral Density
- 5. Gaussian and Other Important Process Families
- 6. Linear Systems Driven by Random Inputs
- 7. Optimum Linear Filtering and Wiener Theory
- 8. Spectral Analysis and Estimation (FFT-based and Parametric Methods)
- 9. Detection and Estimation in Noisy Environments
- 10. Discrete-Time Processes, Time-Series Models, and ARMA Methods
- 11. Adaptive Filtering and Stochastic Gradient Analyses
- 12. Applications to Communications, Radar, and Audio/Speech Systems
- Appendices: Mathematical Tools, Tables, and Worked Exercises
Languages, Platforms & Tools
How It Compares
Comparable to Papoulis's classic treatment of stochastic processes but more application-focused for signals-and-systems engineers; more theoretical depth than Bendat & Piersol's Random Data, while offering many worked exercises.
