Digital Processing of Random Signals: Theory and Methods (Dover Books on Electrical Engineering)
Author Boaz Porat, Professor of Electrical Engineering at the Israel Institute of Technology (Technion), in Haifa, introduces stationary processes and discusses their structure and main properties. He proceeds to examinations of statistical estimation theory, classical spectrum estimation, and parameter estimation theory for Gaussian processes. Subsequent chapters explore autoregressive parameter estimation and its role in adaptive estimation techniques, in addition to estimation methods based on high-order statistical analysis and the time-frequency analysis of nonstationary signals. Four helpful appendixes conclude the text.
Why Read This Book
You will gain a rigorous, mathematically grounded treatment of stochastic signal theory that connects theory to practical estimation and filtering methods used in communications, radar, and audio/speech processing. The book balances deep derivations with numerous homework problems (with hints and selective solutions), so you can both master proofs and practice real-world algorithms.
Who Will Benefit
Graduate students, practicing engineers, and researchers in signal processing, communications, radar, or audio/speech who need a rigorous statistical foundation and practical estimation/filtering tools.
Level: Advanced — Prerequisites: Undergraduate probability and random processes, linear systems and signals, Fourier transforms, and linear algebra; comfort with calculus and complex variables.
Key Takeaways
- Analyze stationary stochastic processes and derive their autocorrelation and spectral representations.
- Design optimal linear estimators including Wiener filtering and state-space (Kalman) estimation for random signals.
- Implement and evaluate classical and modern spectral estimation methods (periodogram, Blackman–Tukey, and parametric AR approaches).
- Model signals using AR/MA/ARMA representations and estimate parameters with methods such as Yule–Walker and maximum likelihood.
- Apply and analyze adaptive filtering algorithms (LMS, RLS), including convergence and misadjustment behavior.
- Formulate and solve statistical detection and parameter estimation problems for Gaussian and near‑Gaussian processes.
Topics Covered
- Mathematical and probabilistic preliminaries
- Stationary processes: definitions, autocorrelation, and properties
- Spectral representation of random processes and the Wiener–Khinchin theorem
- Linear systems driven by random inputs and cross‑spectra
- Wiener filtering and linear estimation theory
- Classical spectral estimation: periodogram and windowed methods
- Parametric spectral estimation: AR/MA/ARMA modeling and methods
- Parameter estimation for Gaussian processes (MLE, Yule–Walker, Burg)
- Adaptive filtering: LMS, RLS, and practical considerations
- State‑space models and Kalman filtering
- Statistical detection, hypothesis testing, and performance bounds
- Exercises, hints, and selected solutions
How It Compares
Covers similar ground to Kay's Modern Spectral Estimation and Haykin's Adaptive Filter Theory but emphasizes rigorous stochastic foundations and comprehensive homework problems rather than extensive implementation code.
