Random Signals: Detection, Estimation and Data Analysis
Random Signals, Noise and Filtering develops the theory of random processes and its application to the study of systems and analysis of random data. The text covers three important areas: (1) fundamentals and examples of random process models, (2) applications of probabilistic models: signal detection, and filtering, and (3) statistical estimation--measurement and analysis of random data to determine the structure and parameter values of probabilistic models. This volume by Breipohl and Shanmugan offers the only one-volume treatment of the fundamentals of random process models, their applications, and data analysis.
Why Read This Book
You should read this book if you need a single, engineering‑oriented reference that ties the mathematics of random processes to practical tasks like detection, estimation and data analysis — you will learn how to model noisy signals, design optimal filters and detectors, and extract parameters from measured data. Its balance of theory, worked examples, and application vignettes makes it especially useful when you must move from stochastic models to implementable DSP and radar/communications solutions.
Who Will Benefit
Advanced undergraduates, graduate students and practicing engineers in DSP, radar, communications or audio/speech who want a compact, application‑focused treatment of random processes, detection and estimation.
Level: Advanced — Prerequisites: Undergraduate calculus and probability/stochastic processes, basic linear systems and Fourier analysis, and linear algebra; familiarity with signals-and-systems concepts and basic programming (MATLAB/Python/C) is helpful.
Key Takeaways
- Model random signals using stationary and nonstationary stochastic process descriptions and compute their power spectral densities.
- Derive and apply optimal detection rules (likelihood ratio tests) and compute detection/false‑alarm tradeoffs and ROC performance.
- Design optimal linear estimators and filters (Wiener filtering) and understand state‑space estimators such as the Kalman filter.
- Perform spectral analysis and parameter estimation using periodograms, parametric (AR) methods and FFT‑based techniques.
- Formulate and solve practical estimation problems including ML and least‑squares parameter estimation and hypothesis testing.
- Apply adaptive filtering concepts to tracking and noise‑cancellation problems and connect theory to radar, communications and audio/speech examples.
Topics Covered
- 1. Introduction to Random Signals and Noise — basic concepts and engineering motivations
- 2. Probability Review and Random Variables — moments, characteristic functions
- 3. Random Processes — stationarity, ergodicity, autocorrelation and cross‑correlation
- 4. Spectral Analysis and Power Spectral Density — Fourier relations, PSD estimation, FFT methods
- 5. Linear Systems Excited by Random Inputs — response, transfer functions and spectral mapping
- 6. Detection Theory — binary detection, likelihood ratio tests, performance metrics
- 7. Linear Estimation and Wiener Filtering — optimal linear estimators in time and frequency domains
- 8. State‑Space Estimation and the Kalman Filter — recursive estimation for dynamic systems
- 9. Statistical Estimation and Parameter Identification — ML, LS, and covariance methods
- 10. Adaptive Filtering Algorithms — LMS, RLS and practical considerations
- 11. Spectral Estimation Techniques — periodogram, averaging, AR modeling and resolution tradeoffs
- 12. Applications: Radar, Communications and Audio/Speech Processing — worked examples and case studies
- 13. Data Analysis and Measurement Considerations — model selection, bias, variance and confidence
Languages, Platforms & Tools
How It Compares
This book provides a compact, application‑focused one‑volume treatment compared with Steven Kay's multi‑volume Fundamentals of Statistical Signal Processing (which is deeper on estimation theory) and Van Trees' Detection, Estimation, and Modulation Theory (which is more exhaustive and theory‑heavy).
