Probability and Random Processes With Applications to Signal Processing
Provides users with an accessible, yet mathematically solid, treatment of probability and random processes. Many computer examples integrated throughout, including random process examples in MATLAB. Includes expanded discussions of fundamental principles, especially basic probability. Includes new problems which deal with applications of basic theory—in such areas as medical imaging, percolation theory in fractals, and generation of random numbers. Several new topics include Failure rates, the Chernoff bound, interval estimation and the Student t-distribution, and power spectral density estimation. Functions of Random Variables is included as a separate chapter. Mean square convergence and introduction of Martingales is covered in the latter half of the book. Provides electrical and computer engineers with a solid treatment of probability and random processes.
Why Read This Book
You will gain a mathematically solid yet practical grounding in probability and random processes tailored to signal-processing problems, with many MATLAB examples that show how theory maps to computation. You will learn how to analyze noise and random signals, estimate spectra, and apply statistical tools (from Chernoff bounds to martingales) that are directly useful for DSP, communications, radar, and audio/speech work.
Who Will Benefit
Graduate students and practicing engineers (signal processing, communications, radar, audio) with undergraduate math looking to apply rigorous probability and random-process theory to real-world signal problems.
Level: Intermediate — Prerequisites: Single-variable calculus, basic multivariable calculus and linear algebra, introductory probability (random variables and distributions), and basic signals-and-systems concepts; familiarity with MATLAB recommended.
Key Takeaways
- Apply probability theory to model and analyze random signals encountered in communications, radar, and audio systems
- Compute and interpret power spectral density and perform spectral analysis using FFT-based and nonparametric estimators
- Use statistical tools—hypothesis testing, interval estimation, Chernoff bounds, and Student's t—for inference in signal-processing problems
- Design and analyze linear systems driven by random inputs, including Wiener filtering and mean-square error criteria
- Simulate and experiment with random processes and algorithms using MATLAB examples to validate analytic results
- Understand convergence concepts (mean-square, limit theorems) and introductory martingales relevant to advanced stochastic analysis
Topics Covered
- Introduction and Fundamentals of Probability
- Random Variables and Distributions
- Functions of Random Variables
- Multiple Random Variables, Vectors, and Joint Distributions
- Conditional Probability, Expectation, and Limit Theorems
- Statistical Inference: Estimation, Confidence Intervals, and the Student t-distribution
- Convergence Modes, Mean-Square Convergence, and Martingales
- Random Processes: Definitions and Basic Properties
- Stationarity, Ergodicity, and Power Spectral Density
- Linear Systems Driven by Random Processes and Wiener Filtering
- Spectral Analysis and FFT-Based Estimation Techniques
- Advanced Topics: Chernoff Bounds, Failure Rates, and Specialized Applications (medical imaging, fractals)
- MATLAB Examples and Simulation Techniques
Languages, Platforms & Tools
How It Compares
Covers similar foundational ground to Papoulis & Pillai's Probability, Random Variables, and Stochastic Processes but is more applied to signal-processing practice with integrated MATLAB examples; for focused estimation/detection theory, Kay's Fundamentals of Statistical Signal Processing is a complementary, more specialized alternative.
