Random Signals and Processes Primer with MATLAB
This book provides anyone needing a primer on random signals and processes with a highly accessible introduction to these topics. It assumes a minimal amount of mathematical background and focuses on concepts, related terms and interesting applications to a variety of fields. All of this is motivated by numerous examples implemented with MATLAB, as well as a variety of exercises at the end of each chapter.
Why Read This Book
You will get a clear, example-driven introduction to random signals and stochastic processes that's designed for engineers who want hands-on understanding rather than heavy theory. The book emphasizes intuition and practical MATLAB experiments so you can simulate, visualize, and apply spectral analysis, filtering, and estimation techniques to audio, radar, and communications problems quickly.
Who Will Benefit
Early-career engineers, graduate students, and practitioners in DSP, communications, radar, or audio/speech processing who need a concise, MATLAB-based grounding in random signals and statistical signal processing.
Level: Beginner — Prerequisites: Basic calculus and linear algebra, elementary signals-and-systems concepts (time/frequency domain, convolution), and familiarity with MATLAB fundamentals (scripts, vectors, plots).
Key Takeaways
- Model and simulate random variables and stochastic processes in MATLAB to build intuition and verify analysis
- Compute and interpret autocorrelation functions, cross-correlations, and power spectral densities using FFT-based and classical spectral-estimation methods
- Analyze the effect of linear systems and digital filters on random inputs and design simple filters to shape stochastic signals
- Apply adaptive filtering and linear prediction techniques to typical DSP tasks such as noise cancellation and system identification
- Use wavelet and time–frequency tools alongside FFT-based methods for nonstationary signal analysis in audio, radar, and communications contexts
Topics Covered
- 1. Introduction and MATLAB Primer
- 2. Probability and Random Variables — a Quick Review
- 3. Random Vectors and Joint Distributions
- 4. Stochastic Processes: Definitions, Stationarity, and Ergodicity
- 5. Moments, Correlation, and Covariance Functions
- 6. Power Spectral Density and FFT-Based Spectral Analysis
- 7. Linear Systems with Random Inputs and Filtering of Random Signals
- 8. Digital Filter Design and Spectral Shaping for Random Signals
- 9. Parametric and Nonparametric Spectral Estimation Methods
- 10. Linear Prediction and Applications to Speech/Audio
- 11. Adaptive Filtering Algorithms and Practical Implementations
- 12. Wavelet-Based and Time–Frequency Analysis of Random Signals
- 13. Applications: Communications, Radar, and Audio/Speech Examples
- 14. MATLAB Examples and End-of-Chapter Exercises
Languages, Platforms & Tools
How It Compares
Compared with Steven Kay's 'Fundamentals of Statistical Signal Processing', this primer is much more accessible and MATLAB-oriented and covers a broader practical introduction rather than deep estimation/detection theory; compared to Papoulis' classic texts, it emphasizes intuition and examples over rigorous proofs.
