Statistical Digital Signal Processing and Modeling
The main thrust is to provide students with a solid understanding of a number of important and related advanced topics in digital signal processing such as Wiener filters, power spectrum estimation, signal modeling and adaptive filtering. Scores of worked examples illustrate fine points, compare techniques and algorithms and facilitate comprehension of fundamental concepts. Also features an abundance of interesting and challenging problems at the end of every chapter.
Why Read This Book
You should read this book if you want a rigorous, example-rich bridge between statistical theory and practical DSP algorithms — from Wiener filters and spectral estimation to AR/MA modeling and adaptive filters. Hayes balances mathematical clarity with numerous worked examples and end-of-chapter problems so you can both understand derivations and apply techniques to real signal processing tasks.
Who Will Benefit
Graduate students, DSP engineers, and researchers who need a solid statistical foundation for spectral analysis, model-based processing, and adaptive filtering in audio, communications, radar, or speech applications.
Level: Advanced — Prerequisites: Undergraduate signals & systems, probability and random processes (stochastic processes), linear algebra, and basic DSP (Fourier transforms, z-transform). Familiarity with MATLAB is helpful for reproducing examples.
Key Takeaways
- Derive and implement Wiener and linear minimum mean-square error (LMMSE) estimators for filtering and prediction.
- Estimate power spectral density using nonparametric (periodogram, windowing, Welch) and parametric (AR/ARMA) methods and assess bias/variance tradeoffs.
- Build and validate AR, MA and ARMA signal models and perform model-order selection and diagnostics.
- Design and analyze adaptive algorithms (LMS, NLMS, RLS) and understand their convergence and performance characteristics.
- Apply model-based techniques (linear prediction, prewhitening) to practical problems in speech, audio, and communications.
- Quantify statistical properties of estimators (bias, variance, covariance) and use them to choose/compare algorithms.
Topics Covered
- 1. Introduction and Mathematical Background (Random Processes & Second-Order Theory)
- 2. Stationary Processes, Autocorrelation, and Cross-correlation
- 3. Power Spectral Density and the Fourier Transform of Random Signals
- 4. Linear Prediction and Wiener Theory
- 5. Parametric Signal Modeling: AR, MA and ARMA Models
- 6. Parameter Estimation Methods (Yule-Walker, Burg, Least Squares)
- 7. Model Order Selection and Model Validation
- 8. Nonparametric Spectral Estimation (Periodogram, Windowing, Welch, Multitaper)
- 9. Parametric Spectral Estimation and High-resolution Methods
- 10. Adaptive Filtering: LMS, NLMS, RLS and Variants
- 11. Practical Issues: Prewhitening, Spectral Smoothing, Numerical Considerations
- 12. Applications and Examples (Speech, Audio, Communications, Radar)
- 13. Worked Examples and End-of-Chapter Problems
Languages, Platforms & Tools
How It Compares
Covers broader modeling and adaptive-filter topics than Steven Kay's Modern Spectral Estimation (which is stronger on estimation theory) and is more application-oriented across modeling/adaptive filtering than Stoica & Moses' Spectral Analysis (which is more advanced and linear-algebra centric).
