Introduction to random processes: With applications to signals and systems
This book was written as a graduate level textbook for engineering students who have had a course in probability and random variables intended for students of engineering or the physical sciences. It is focused primarily on random processes as models for randomly time-varying signals and noise.
Why Read This Book
You will learn how to model and analyze randomly time-varying signals using a rigorous, engineering-focused treatment of stochastic processes, with a strong emphasis on second‑order statistics (autocorrelation and power spectral density). The book connects probabilistic concepts directly to practical signal‑processing tasks—spectral analysis, filtering, and noise modeling—making it valuable when you need principled tools for DSP, communications, radar, or audio/speech problems.
Who Will Benefit
Graduate students and practicing engineers with a basic probability background who need to apply stochastic process theory to DSP, communications, radar, or audio/speech problems.
Level: Advanced — Prerequisites: A course in probability and random variables, comfort with calculus and linear systems, and familiarity with Fourier transforms and basic signal processing concepts.
Key Takeaways
- Analyze stationary and ergodic processes using autocorrelation functions and power spectral densities
- Apply the Wiener–Khinchin relationships and spectral factorization to connect time‑domain and frequency‑domain descriptions
- Predict and estimate signals with linear estimators (Wiener filtering/prediction) in the presence of stochastic noise
- Model common engineering noise sources and understand Gaussian and related process classes used in communications, radar, and audio
- Perform spectral analysis of random signals and interpret results for practical tasks like detection, system identification, and performance prediction
- Formulate second‑order descriptions (covariance, cross‑spectra) for multichannel and filtered random processes
Topics Covered
- 1. Introduction: Random Processes in Engineering
- 2. Review of Probability and Random Variables
- 3. Definitions and Classifications of Random Processes
- 4. Stationarity, Ergodicity, and Moments
- 5. Autocorrelation and Cross‑correlation Functions
- 6. Power Spectral Density and the Wiener–Khinchin Theorem
- 7. Linear Systems Driven by Random Inputs
- 8. Gaussian Processes and Important Special Cases
- 9. Spectral Factorization and Linear Prediction
- 10. Wiener Filtering and Optimal Linear Estimation
- 11. Applications to Communications, Radar, and Audio/Speech Signals
- 12. Appendix: Mathematical Tools and Transform Relations
Languages, Platforms & Tools
How It Compares
Covers similar ground to Papoulis' Probability, Random Variables, and Stochastic Processes but places greater emphasis on second‑order methods and signal‑processing applications; for a more measure‑theoretic treatment, consult Doob's Stochastic Processes.
