Stationary Stochastic Processes for Scientists and Engineers
Stochastic processes are indispensable tools for development and research in signal and image processing, automatic control, oceanography, structural reliability, environmetrics, climatology, econometrics, and many other areas of science and engineering. Suitable for a one-semester course, Stationary Stochastic Processes for Scientists and Engineers teaches students how to use these processes efficiently. Carefully balancing mathematical rigor and ease of exposition, the book provides students with a sufficient understanding of the theory and a practical appreciation of how it is used in real-life situations. Special emphasis is on the interpretation of various statistical models and concepts as well as the types of questions statistical analysis can answer.
The text first introduces numerous examples from signal processing, economics, and general natural sciences and technology. It then covers the estimation of mean value and covariance functions, properties of stationary Poisson processes, Fourier analysis of the covariance function (spectral analysis), and the Gaussian distribution. The book also focuses on input-output relations in linear filters, describes discrete-time auto-regressive and moving average processes, and explains how to solve linear stochastic differential equations. It concludes with frequency analysis and estimation of spectral densities.
With a focus on model building and interpreting the statistical concepts, this classroom-tested book conveys a broad understanding of the mechanisms that generate stationary stochastic processes. By combining theory and applications, the text gives students a well-rounded introduction to these processes. To enable hands-on practice, MATLAB® code is available online.
Why Read This Book
You will learn how stationary stochastic processes provide the mathematical foundation for spectral analysis, filtering, prediction, and statistical inference used across audio/speech, radar, and communications engineering. The book balances mathematical rigor with practical interpretation so you can both derive key results and apply them to real signal-processing problems.
Who Will Benefit
Graduate students and practicing engineers with undergraduate training in signals, probability, or applied math who need to apply stationary stochastic-process theory to DSP, radar, audio/speech, or communications problems.
Level: Intermediate — Prerequisites: Undergraduate calculus and linear algebra, basic probability and random variables, and introductory Fourier/transform and signals-and-systems concepts; familiarity with basic statistical concepts is helpful.
Key Takeaways
- Characterize stationary processes in time and frequency by deriving autocorrelation functions and power spectral densities
- Apply the spectral representation theorem and Fourier methods to perform rigorous spectral analysis
- Design and analyze linear filters and predictors using Wiener–Kolmogorov theory and understand their performance in noisy environments
- Estimate model parameters and spectra from data (periodogram, parametric ARMA estimation) and assess statistical properties of estimators
- Model multivariate and continuous-time stationary processes and assess ergodicity and asymptotic behavior for inference
- Interpret statistical models for real engineering applications such as audio/speech processing, radar signal analysis, and communications channel modeling
Topics Covered
- 1. Introduction: Applications and motivation in science and engineering
- 2. Probability preliminaries and random processes
- 3. Stationarity, moments, and ergodicity
- 4. Autocovariance, correlation functions, and basic properties
- 5. Spectral representation and power spectral density
- 6. Linear processes and filtering of stationary sequences
- 7. AR, MA and ARMA models: properties and representations
- 8. Prediction theory and Wiener–Kolmogorov filtering
- 9. Estimation of spectra and model parameters (periodogram, parametric methods)
- 10. Multivariate stationary processes and cross-spectral analysis
- 11. Continuous-time stationary processes
- 12. Asymptotic theory, inference, and hypothesis testing
- 13. Examples and engineering applications (audio/speech, radar, communications)
- Appendices: Fourier transforms, linear algebra and supplementary mathematics
Languages, Platforms & Tools
How It Compares
Compared to Brockwell & Davis's comprehensive time-series theory, Lindgren is more application-oriented and geared toward engineering interpretation; compared with Hayes's DSP-focused text, Lindgren emphasizes stochastic-process foundations rather than implementation of spectral algorithms.
