Statistical Signal Processing: Detection, Estimation, and Time Series Analysis
This book embraces the many mathematical procedures that engineers and statisticians use to draw inference from imperfect or incomplete measurements. This book presents the fundamental ideas in statistical signal processing along four distinct lines: mathematical and statistical preliminaries; decision theory; estimation theory; and time series analysis.
Why Read This Book
You should read this book if you want a compact, mathematically disciplined presentation of detection and estimation fundamentals that underlie many DSP algorithms. It sharpens your ability to derive and justify hypothesis tests, estimators, and time-series models rather than just apply recipes.
Who Will Benefit
Graduate students and practicing engineers working on detection/estimation, radar/communications, or spectral/time-series analysis who need a rigorous theoretical reference.
Level: Advanced — Prerequisites: Linear algebra, probability & random processes, calculus, and basic signals-and-systems knowledge (Fourier transforms and stochastic processes).
Key Takeaways
- Formulate hypothesis tests and derive likelihood-ratio and Bayes detectors for common signal-plus-noise models.
- Derive and analyze point estimators (ML, LS, BLUE) and compute performance bounds such as the Cramér–Rao bound.
- Design linear estimators and filters (Wiener/linear minimum mean square error) for stationary and nonstationary processes.
- Model and analyze time series (AR/MA/ARMA) and perform related spectral-estimation tasks.
- Apply multichannel and structured-model approaches to detection and estimation problems common in radar and communications.
Topics Covered
- Mathematical and Statistical Preliminaries
- Random Vectors and Matrices
- Decision Theory and Hypothesis Testing
- Detection of Deterministic and Stochastic Signals
- Estimation Theory: Point and Interval Estimation
- Linear Estimation and Wiener Filtering
- Maximum Likelihood and Method-of-Moments
- Performance Bounds and Cramér–Rao Inequalities
- Time-Series Models and ARMA Processes
- Spectral Estimation Methods
- Multichannel Models and Structured Estimation
- Sequential Estimation and Recursive Filters
- Applications and Worked Examples
How It Compares
Covers similar ground to Van Trees' classical Detection and Estimation and to Steven Kay's Fundamentals of Statistical Signal Processing, but Scharf is more concise and mathematically focused rather than a step-by-step tutorial.
