Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers
This text introduces engineering students to probability theory and stochastic processes. Along with thorough mathematical development of the subject, the book presents intuitive explanations of key points in order to give students the insights they need to apply math to practical engineering problems. The first seven chapters contain the core material that is essential to any introductory course. In one-semester undergraduate courses, instructors can select material from the remaining chapters to meet their individual goals. Graduate courses can cover all chapters in one semester.
Why Read This Book
You will get a clear, engineering-first introduction to probability and stochastic processes that emphasizes intuition and practical application to DSP, communications, and radar problems. The book balances rigorous development with worked examples so you can move from theory to modeling noise, spectra, and estimators used in real systems.
Who Will Benefit
Upper-level undergraduate or beginning graduate electrical and computer engineers who need to model and analyze random signals and systems for DSP, communications, radar, or networking applications.
Level: Intermediate — Prerequisites: Single- and multivariable calculus, basic linear algebra, and introductory signals & systems or familiarity with Fourier transforms; basic exposure to deterministic signals and systems is helpful.
Key Takeaways
- Model random signals and processes relevant to DSP and communications using stationarity, ergodicity, and correlation concepts
- Compute power spectral densities and apply spectral analysis tools (autocorrelation, Fourier transforms) to characterize noise and signals
- Analyze the response of linear systems to stochastic inputs and design/understand optimal linear estimators and filters (e.g., Wiener filtering)
- Formulate and solve basic detection and estimation problems for signals in noise, including probabilistic error analysis
- Use Markov, Poisson, and renewal process models to analyze discrete-event systems and queuing behavior in communications and radar contexts
Topics Covered
- Probability fundamentals: axioms, combinatorics, conditional probability
- Random variables and expectation: distributions, moments, transforms
- Multiple random variables: joint distributions, independence, transforms
- Convergence, laws of large numbers, and central limit theorem
- Conditional expectation and useful inequalities
- Random processes: definitions, stationarity, ergodicity
- Correlation functions and power spectral density
- Linear systems driven by random inputs and spectral factorization
- Gaussian processes, noise models, and passage through systems
- Detection and estimation theory: basics for signals in noise
- Point processes: Poisson processes and renewal theory
- Markov chains, queuing models, and applications to networks
Languages, Platforms & Tools
How It Compares
More conversational and application-oriented than Papoulis' classic treatment, and somewhat more concise and engineering-focused than Leon-Garcia's coverage of random processes.
