Probability and Random Processes: With Applications to Signal Processing and Communications
Probability and Random Processes, Second Edition presents pertinent applications to signal processing and communications, two areas of key interest to students and professionals in today's booming communications industry. The book includes unique chapters on narrowband random processes and simulation techniques. It also describes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and others.
Exceptional exposition and numerous worked out problems make this book extremely readable and accessible. The authors connect the applications discussed in class to the textbook. The new edition contains more real world signal processing and communications applications. It introduces the reader to the basics of probability theory and explores topics ranging from random variables, distributions and density functions to operations on a single random variable. There are also discussions on pairs of random variables; multiple random variables; random sequences and series; random processes in linear systems; Markov processes; and power spectral density.
This book is intended for practicing engineers and students in graduate-level courses in the topic.
- Exceptional exposition and numerous worked out problems make the book extremely readable and accessible
- The authors connect the applications discussed in class to the textbook
- The new edition contains more real world signal processing and communications applications
- Includes an entire chapter devoted to simulation techniques
Why Read This Book
You will get a rigorous yet application-focused grounding in probability and stochastic processes tailored to signal processing and communications problems. The book pairs clear exposition and many worked examples with unique chapters on narrowband random processes and simulation techniques so you can move quickly from theory to practical analysis and Monte Carlo experiments.
Who Will Benefit
Graduate students, advanced undergraduates, and practicing engineers in signal processing, communications, radar, or audio/speech who need to apply probabilistic methods to real-world systems.
Level: Intermediate — Prerequisites: Calculus (including multivariable), linear algebra, basic signals and systems (Fourier transforms, LTI systems), and introductory probability (random variables and distributions).
Key Takeaways
- Understand the probabilistic foundations needed to model noise and random signals in DSP and communications.
- Analyze and compute autocorrelation, power spectral density, and perform spectral estimation using FFT-based methods.
- Design and analyze linear filters and Wiener solutions for stochastic inputs, including narrowband random process models.
- Implement and validate Monte Carlo simulation techniques for signal processing and communications problems.
- Apply detection, estimation, and basic information-theoretic concepts to practical communication and radar scenarios.
Topics Covered
- Introduction and Review of Probability Concepts
- Random Variables and Probability Distributions
- Multivariate Distributions, Characteristic and Moment-Generating Functions
- Convergence, Laws of Large Numbers and Central Limit Theorems
- Random Processes: Definitions, Stationarity and Ergodicity
- Autocorrelation Functions and Power Spectral Density (Wiener–Khintchine)
- Linear Systems with Random Inputs and Wiener Filtering
- Narrowband Random Processes and Complex Envelope Representations
- Spectral Analysis, FFTs and Parametric/Nonparametric Spectral Estimation
- Adaptive Filtering and LMS-type Algorithms
- Detection and Estimation Basics for Communications and Radar
- Applications: Digital Communications, Coding, Image, Speech and Audio Processing
- Simulation Techniques and Monte Carlo Methods
- Appendices: Mathematical Tools and Solution Hints
Languages, Platforms & Tools
How It Compares
More application-oriented than Papoulis & Pillai's classic text and broader in scope than Kay's estimation-focused volumes — it balances theory, worked examples, and simulation for DSP/communications engineers.
