Why Read This Book

You will gain a rigorous, engineering-focused grounding in probability and stochastic processes tailored to signal-processing and communications problems. The book emphasizes intuition and worked examples that connect abstract probability concepts to practical tasks like spectral analysis, filtering of random signals, and noise modeling.

Who Will Benefit

Upper-level undergraduate and graduate electrical engineers, DSP and communications engineers, and researchers who need a solid, application-oriented foundation in probability and random processes for analyzing signals and systems.

Level: Intermediate — Prerequisites: Single-variable and multivariable calculus, basic linear algebra, signals and systems fundamentals (Fourier and Laplace transforms), and introductory deterministic signals/filters; familiarity with basic probability is helpful but not strictly required.

Key Takeaways

• Describe and manipulate probability distributions and transforms used in engineering (PDFs, CDFs, characteristic and moment-generating functions).
• Analyze stochastic processes and apply stationarity, ergodicity, autocorrelation, and power spectral density concepts to real signals.
• Predict and compute the response of linear systems to random inputs, including noise propagation and filtering effects.
• Model common random processes in communications and radar (Gaussian processes, Poisson processes, and Markov chains) and use them in performance calculations.
• Apply limit theorems and statistical tools to assess estimators, detection problems, and the asymptotic behavior of random sequences.

Topics Covered

1. 1. Introduction to Probability and Engineering Examples
2. 2. Random Variables and Their Distributions
3. 3. Joint Distributions, Independence, and Conditional Probability
4. 4. Functions of Random Variables and Transform Methods
5. 5. Expectations, Moments, and Inequalities
6. 6. Limit Theorems and Convergence Concepts
7. 7. Introduction to Random Processes and Classification
8. 8. Stationarity, Ergodicity, and Correlation Functions
9. 9. Spectral Analysis and Power Spectral Density
10. 10. Linear Systems with Random Inputs and Filtering of Noise
11. 11. Gaussian Processes and Properties of Jointly Gaussian Vectors
12. 12. Poisson Processes and Renewal Theory
13. 13. Markov Chains and Continuous-Time Markov Processes
14. 14. Detection, Estimation, and Statistical Decision Concepts
15. 15. Applications to Communications, Radar, and Signal Processing

Languages, Platforms & Tools

How It Compares

Covers similar applied EE-focused ground as Papoulis' Probability, Random Variables, and Stochastic Processes but with more engineering examples and a different pedagogical emphasis; more application-oriented than pure-math texts and complementary to Stark & Woods' treatments that include more simulation-focused exercises.