Why Read This Book

You should read this book if you need a rigorous, engineering-focused grounding in probability, random processes, and estimation theory that you can directly apply to DSP, communications, radar, and audio/speech problems. You will learn how to model stochastic signals, analyze their spectra, and design practical estimators and filters (Wiener, Kalman, ML) with worked examples and clear connections to real signal-processing systems.

Who Will Benefit

Practicing engineers and graduate students with some calculus and linear algebra who design or analyze DSP, communications, radar, or audio/speech systems and need a solid theoretical foundation for stochastic modeling and estimation.

Level: Advanced — Prerequisites: Single-variable and multivariable calculus, linear algebra (vectors, matrices, eigenvalues), basic deterministic signals and systems, and introductory probability (random variables and distributions).

Key Takeaways

• Model stochastic signals and systems using random processes and power spectral density concepts applicable to audio, radar, and communications.
• Analyze and compute spectral estimates (periodogram, correlogram) and relate them to linear system responses and FFT-based methods.
• Derive and implement optimal linear estimators including Wiener and Kalman filters for stationary and non-stationary processes.
• Formulate and solve parameter estimation and hypothesis testing problems (MLE, MVU, CRLB, detection theory) relevant to signal processing tasks.
• Apply statistical tools to design adaptive filters and assess performance limits in noisy environments using covariance and correlation methods.

Topics Covered

1. 1. Probability Fundamentals and Random Variables
2. 2. Joint Distributions, Transform Methods, and Limit Theorems
3. 3. Functions of Random Variables and Inequalities
4. 4. Introduction to Random Processes
5. 5. Stationary Processes, Autocorrelation, and Ergodicity
6. 6. Power Spectral Density and Spectral Representations
7. 7. Linear Systems Driven by Random Processes
8. 8. Spectral Estimation and the FFT in Stochastic Analysis
9. 9. Parameter Estimation: Method of Moments and Maximum Likelihood
10. 10. Properties of Estimators, Cramér–Rao Bounds, and Efficiency
11. 11. Detection and Hypothesis Testing for Signals in Noise
12. 12. Wiener Filtering, Adaptive Filtering, and Kalman Filtering
13. 13. Applications to Communications, Radar, and Audio/Speech Processing
14. Appendices: Mathematical Background and Useful Integrals

Languages, Platforms & Tools

How It Compares

Covers the same foundational material as Papoulis's classic but with a more engineering-oriented revision and stronger emphasis on estimation theory; for focused estimation and detection treatment compare Kay's 'Fundamentals of Statistical Signal Processing.'