Why Read This Book

You will gain a rigorous, probability-first foundation for analyzing and processing random signals, with clear derivations that connect theory to practical DSP tasks. The book grounds estimation, detection, spectral analysis, and adaptive filtering in statistical principles you can apply to audio/speech, radar, and communications problems.

Who Will Benefit

Graduate students and practicing DSP, communications, radar or audio engineers who need a solid probabilistic foundation to design and analyze estimation, detection, spectral and adaptive-signal-processing algorithms.

Level: Intermediate — Prerequisites: Multivariable calculus, linear algebra, and basic probability (random variables and distributions); familiarity with signals & systems (discrete-time Fourier transform and basic filtering).

Key Takeaways

• Apply probabilistic models and random-process concepts to analyze signals and noise.
• Derive and implement minimum mean-square-error (MMSE), maximum-likelihood (ML) estimators and hypothesis tests for detection problems.
• Design and analyze linear estimators and predictors including Wiener and Kalman filters.
• Perform spectral analysis and estimation using FFT-based methods and parametric techniques.
• Implement and evaluate adaptive filtering algorithms (LMS, RLS) and characterize their convergence and performance.
• Use time–frequency and wavelet approaches to handle nonstationary signals in practical DSP applications.

Topics Covered

1. 1. Introduction and Overview of Statistical Signal Processing
2. 2. Review of Probability and Random Variables
3. 3. Random Processes: Definitions, Stationarity, and Ergodicity
4. 4. Second-Order Properties and Covariance Functions
5. 5. Spectral Representation and Spectral Analysis
6. 6. Discrete Fourier Transform, FFT, and Practical Spectral Estimators
7. 7. Linear Prediction and Wiener Filtering
8. 8. Kalman Filtering and State-Space Estimation
9. 9. Detection Theory and Hypothesis Testing
10. 10. Parameter Estimation and Maximum Likelihood Methods
11. 11. Adaptive Filtering: LMS, RLS, and Extensions
12. 12. Time–Frequency Methods and Wavelets for Nonstationary Signals
13. 13. Applications: Communications, Radar, and Audio/Speech Examples
14. Appendices: Mathematical Tools and Reference Material

Languages, Platforms & Tools

How It Compares

Covers similar foundational ground to S. M. Kay's Fundamentals of Statistical Signal Processing but is more introductory/accessible and broader in DSP applications; it is less exhaustive than the multivolume, mathematically-heavy treatments by Van Trees.