Probabilistic Systems and Random Signals
In-depth mathematical treatment, including examples of real systems to explain many of the probabilistic models and the use of Matlab both in examples and problem assignments, ensures students can relate to the mathematical material in practical terms Unique applications—covering issues such as reliability, measurement errors, and arrival and departure of events in networks—provide students with a broader range of topical coverage.
Why Read This Book
You will gain a rigorous, system-level understanding of stochastic signals and probabilistic methods that underpin modern DSP, communications, radar, and measurement systems. The book blends thorough mathematical development with MATLAB examples and realistic applications (reliability, measurement error, network arrivals), so you can move directly from theory to simulation and engineering practice.
Who Will Benefit
Advanced undergraduates, graduate students, and practicing engineers with basic signals/probability knowledge who need to model, analyze, and simulate random signals in communications, radar, audio, and measurement systems.
Level: Advanced — Prerequisites: Calculus (including multivariable), linear algebra, basic probability and random variables, signals and systems fundamentals, and familiarity with MATLAB for running examples and assignments.
Key Takeaways
- Model random signals and systems using rigorous probabilistic frameworks (random variables, vectors, and processes).
- Apply spectral analysis and FFT-based methods to characterize stationary and nonstationary random processes.
- Design and analyze linear estimators and detectors (Wiener, least-squares, and basic Kalman concepts) for noisy measurement systems.
- Implement and evaluate adaptive filtering algorithms and study their convergence and steady-state behavior.
- Use MATLAB to simulate stochastic systems, reproduce textbook examples, and solve assigned engineering problems.
- Analyze practical applications such as reliability issues, measurement error modeling, and arrival/departure processes in networks.
Topics Covered
- 1. Introduction to Probabilistic Modeling and Random Signals
- 2. Random Variables and Probability Distributions
- 3. Random Vectors and Multivariate Techniques
- 4. Random Processes: Definitions and Properties
- 5. Stationary Processes and Autocorrelation Functions
- 6. Spectral Analysis, Power Spectral Density, and the FFT
- 7. Linear Systems Driven by Random Inputs
- 8. Estimation Theory: Least Squares and Wiener Filters
- 9. Detection Basics and Hypothesis Testing for Signals in Noise
- 10. Adaptive Filtering and Stochastic Gradient Methods
- 11. Wavelets and Time–Frequency Representations for Random Signals
- 12. Applications: Communications, Radar, Audio/Speech, and Measurement Errors
- 13. Reliability, Queuing, and Arrival/Departure Modeling in Networks
- 14. MATLAB Examples, Problem Sets, and Numerical Techniques
- Appendices: Mathematical Tools and Transform Tables
Languages, Platforms & Tools
How It Compares
Covers similar ground to Papoulis' 'Probability, Random Variables, and Stochastic Processes' and Peebles' classic text, but Haddad emphasizes system-oriented applications and extensive MATLAB examples tied to reliability and network arrival models.
