Why Read This Book

You will learn how to model, analyze, and process discrete-time stochastic signals with a practical emphasis on algorithms you can implement. This book combines rigorous statistical foundations with worked examples and applied techniques (spectral estimation, adaptive filtering, detection) so you can move from theory to real DSP systems in audio, communications, and radar.

Who Will Benefit

Practicing engineers and graduate students with a solid math background who need to apply statistical signal processing and stochastic modeling to audio/speech, radar, or communications problems.

Level: Advanced — Prerequisites: Undergraduate calculus and linear algebra, basic probability and random variables, introductory digital signal processing (discrete-time systems, z-transform, FFT); familiarity with MATLAB or similar numerical tools is strongly recommended.

Key Takeaways

• Model discrete random processes and compute their second-order statistical properties (autocorrelation, covariance, PSD)
• Derive how linear systems affect stochastic inputs and predict output statistics
• Design and analyze spectral estimation methods (periodogram, Welch, AR/MA/ARMA parametric methods)
• Formulate and implement optimal linear estimators and predictors (Wiener filtering, linear MMSE)
• Apply adaptive filtering algorithms (LMS, RLS) for noise cancellation, tracking, and system identification
• Use statistical detection and estimation principles in communications and radar signal-processing tasks

Topics Covered

1. 1. Introduction and Overview of Discrete Random Signals
2. 2. Review of Probability and Random Variables
3. 3. Discrete-Time Stochastic Processes and Stationarity
4. 4. Autocorrelation, Covariance, and Power Spectral Density
5. 5. Linear Systems with Random Inputs
6. 6. Spectral Analysis and Estimation Techniques
7. 7. Parametric Models: AR, MA, and ARMA Processes
8. 8. Optimal Linear Prediction and Wiener Filtering
9. 9. Adaptive Filters: LMS, RLS, and Convergence Issues
10. 10. Statistical Detection and Estimation for Signals in Noise
11. 11. Applications: Audio/Speech, Radar, and Communications Examples
12. 12. Numerical Methods, Algorithms, and Software Considerations
13. Appendices: Mathematical Tools and Tables, Disk Files/Code Notes

Languages, Platforms & Tools

How It Compares

Covers similar practical ground to A. Papoulis/H. Pillai-style stochastic treatments and Hayes' Statistical Digital Signal Processing, but is more implementation-oriented with worked examples and application notes; for a deeper theoretical treatment of detection/estimation see Kay's 'Fundamentals of Statistical Signal Processing.'