An Introduction to the Theory of Random Signals and Noise
This "bible" of a whole generation of communications engineers was originally published in 1958. The focus is on the statistical theory underlying the study of signals and noises in communications systems, emphasizing techniques as well s results. End of chapter problems are provided. Sponsored by: IEEE Communications Society
Why Read This Book
You should read this book if you want a clear, communications-focused grounding in the statistical theory of random signals and noise — the mathematical foundations that underpin modern DSP, detection, and estimation. It emphasizes techniques and worked problems that make abstract stochastic ideas practical for engineers working on communications, radar, and spectral analysis.
Who Will Benefit
Advanced undergraduates, graduate students, and practicing communications/DSP engineers seeking a rigorous, application-minded introduction to stochastic signal theory and noise in systems.
Level: Advanced — Prerequisites: Undergraduate calculus, linear systems (signals & systems), basic probability and random variables; familiarity with Fourier transforms and complex exponentials.
Key Takeaways
- Derive and interpret autocorrelation functions and power spectral densities for stationary random processes.
- Analyze the response of linear time-invariant systems to random inputs and compute output statistics.
- Apply Gaussian-process properties to simplify performance analysis for common noise models.
- Design and analyze optimal linear estimators/filters (Wiener theory) for minimum-mean-square-error tasks.
- Understand the principles behind matched filtering and basic detection/estimation in noisy channels.
- Perform elementary spectral analysis and sampling considerations for random signals.
Topics Covered
- 1. Introduction and Motivation: Signals, Noise, and Randomness
- 2. Random Variables and Basic Probability Concepts
- 3. Definitions and Properties of Random Processes
- 4. Stationarity, Ergodicity, and Ensemble vs. Time Averages
- 5. Autocorrelation Functions and Power Spectral Density
- 6. Linear Systems Driven by Random Inputs
- 7. Gaussian Random Processes and Their Importance
- 8. Noise in Communication Systems and Basic Models
- 9. Detection Concepts and the Correlation Receiver / Matched Filter
- 10. Wiener Filtering and Linear MMSE Estimation
- 11. Spectral Estimation and Practical Considerations
- 12. Sampling of Random Signals and Aliasing
- Appendices, Problems, and Tables
How It Compares
Covers similar ground to Papoulis's treatment of stochastic processes but with a stronger communications engineering focus and more applied examples; less exhaustive in detection/estimation theory than Van Trees' multi-volume work.
