Random Processes for Engineers
This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).
Why Read This Book
You will get an intuitive, engineering-focused introduction to random processes that balances practical signal-processing tools with clear explanations of underlying measure-aware concepts. You will learn how to analyze stochastic inputs to linear systems and apply core algorithms (Wiener/Kalman/HMM) to real DSP, communications, and radar problems.
Who Will Benefit
Graduate or advanced undergraduate engineers and practitioners in signal processing, communications, or controls who need to design or analyze systems operating under uncertainty.
Level: Intermediate — Prerequisites: Basic probability and random variables, multivariable calculus, linear systems (signals and systems), and linear algebra; prior exposure to basic DSP concepts is helpful.
Key Takeaways
- Analyze random processes in time and frequency and relate second-order statistics to spectral behavior
- Apply Wiener and Kalman filtering to design optimal linear estimators for noisy linear systems
- Use sampling and asymptotic tools to manage complexity and approximate stochastic behaviors
- Formulate and perform inference with Hidden Markov Models for sequence data
- Implement practical spectral-analysis and filtering approaches relevant to audio, radar, and communications
Topics Covered
- 1. Review of Probability and Deterministic Function Analysis
- 2. Foundations of Random Variables and Vectors
- 3. Classes of Random Processes: Stationarity and Ergodicity
- 4. Second-Order Theory and Correlation Functions
- 5. Spectral Analysis and the Fourier/FFT View of Random Processes
- 6. Linear Systems Driven by Random Inputs
- 7. Sampling of Random Processes and Aliasing Effects
- 8. Wiener Filtering and Prediction
- 9. Kalman Filtering and State-Space Estimation
- 10. Hidden Markov Models and Statistical Inference
- 11. Adaptive Filtering and Practical Algorithms
- 12. Large-Sample and Asymptotic Methods
- 13. Applications: Audio/Speech, Radar, and Communications Examples
Languages, Platforms & Tools
How It Compares
More modern and intuitively measure-aware than Papoulis' classic treatment and broader in systems perspective than Steven Kay's estimation-focused Fundamentals of Statistical Signal Processing.
