Stochastic Processes

(Introductory course with applications on signal analysis and control)

Description

This course provides an integrated introduction to signals, systems, stochastic processes, Fourier analysis, digital signal processing, control systems, and time-series modeling. The course begins with the characterization of continuous-time and discrete-time signals and systems, including LTI systems, Laplace and z-transform methods, block-diagram algebra, sampling, quantization, and filter design. It then develops the foundations of probability, random vectors, random processes, Gaussian processes, and spectral analysis of random signals.

The course concludes with statistical signal processing, time-series forecasting, and stochastic state-space methods, with practical implementation in Python and MATLAB/Octave for engineering applications in signal analysis, estimation, detection, and control.

Outline

Unit 1. Fundamentals of Signals and Systems

Unit 2. Continuous-Time LTI Systems and Laplace Transform

Unit 3. Discrete-Time LTI Systems and z-Transform

Unit 4. Sampling and Digital Signal Processing

Unit 5. Fourier Series and Harmonic Analysis

Unit 6. Fourier Transform and Frequency-Domain Analysis

Unit 7. Filter Design and Frequency-Domain Processing

Unit 8. Probability Foundations for Signal Processing

Unit 9. Random Processes and Stochastic Signal Models

Unit 10. Correlation and Spectral Analysis of Random Signals

Unit 11. Stochastic Systems and Control

Unit 12 Applications

[1] Alan V Oppenheim, Ronald W. Schafer, Discrete-Time Signal Processing: Pearson New International, Edition 3, 2014, Person.
[2] Hwei Hsu, Schaum’s Outline of Signals and Systems, Edition 4, 2020, McGraw-Hill Education.
[3] George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel, Greta M. Ljung,Time Series Analysis: Forecasting and Control, Edition 5, 2015, Prentice Hall.