Probabilistic Methods of Signal and System Analysis (The ^AOxford Series in Electrical and Computer Engineering)
Probabilistic Methods of Signal and System Analysis, 3/e stresses the engineering applications of probability theory, presenting the material at a level and in a manner ideally suited to engineering students at the junior or senior level. It is also useful as a review for graduate students and practicing engineers.
Thoroughly revised and updated, this third edition incorporates increased use of the computer in both text examples and selected problems. It utilizes MATLAB as a computational tool and includes new sections relating to Bernoulli trials, correlation of data sets, smoothing of data, computer computation of correlation functions and spectral densities, and computer simulation of systems. All computer examples can be run using the Student Version of MATLAB. Almost all of the examples and many of the problems have been modified or changed entirely, and a number of new problems have been added. A separate appendix discusses and illustrates the application of computers to signal and system analysis.
Why Read This Book
You should read this book if you want a practical, engineering-focused introduction to using probability and random-process theory to analyze signals and systems; you will learn how probabilistic tools guide design and performance assessment of filters, spectral estimators, detectors, and adaptive algorithms. The text emphasizes real-world application with MATLAB examples and computer simulation, so you will gain hands-on skills for implementing DSP and statistical-signal-processing methods.
Who Will Benefit
Ideal for junior/senior electrical engineering undergraduates, graduate students seeking a review, or practicing engineers who need a practical, MATLAB-oriented treatment of probabilistic signal analysis.
Level: Intermediate — Prerequisites: Single-variable calculus, basic linear systems and signals (LTI systems, convolution), introductory probability and statistics (random variables, mean/variance); familiarity with MATLAB is helpful but not strictly required.
Key Takeaways
- Apply probabilistic descriptions to signals and systems, modeling signals as random processes and interpreting mean, autocorrelation, and stationarity measures.
- Compute and interpret power spectral densities using FFT-based and parametric methods, and implement spectral estimation in MATLAB.
- Design and analyze linear estimators and filters (Wiener, matched filtering) and evaluate their performance in noise.
- Implement and test adaptive filtering algorithms (e.g., LMS-type) and assess convergence and tracking via simulation.
- Use Monte Carlo simulation and MATLAB to validate theoretical results, compute correlation functions, and approximate detection and estimation metrics.
Topics Covered
- Introduction: Role of Probability in Signal and System Analysis
- Review of Probability and Random Variables
- Multiple Random Variables and Vector Gaussian Distributions
- Random Processes: Stationarity, Ergodicity, and Correlation Functions
- Spectral Analysis: Power Spectral Density and the Fourier Transform
- Discrete-Time Random Processes and FFT-Based Spectral Estimation
- Linear Estimation and Detection: Wiener and Matched Filters
- Digital Filtering and Performance in Noise
- Adaptive Filtering and Algorithms (LMS and variants)
- Parametric Methods and AR/MA Modeling
- Statistical Signal Processing Techniques and Hypothesis Testing
- Computer Methods: MATLAB Examples, Monte Carlo Simulation, and Data Smoothing
- Applications: Communications, Audio/Speech, and Radar Signal Examples
- Appendices: Mathematical Background and MATLAB Primer
Languages, Platforms & Tools
How It Compares
Compared with Papoulis' Probability, Random Variables, and Stochastic Processes, Cooper is more application- and MATLAB-oriented and is pitched at engineering undergraduates; for a deeper, specialist treatment of statistical signal processing theory and detection/estimation, Kay's Fundamentals of Statistical Signal Processing is a more advanced complement.
