619-007 Stochastic Processes for Electrical Engineers

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Objectives:

To introduce students to multivariate distributions and simple stochastic processes and thence basic time series analysis using both time domain and spectral methods. This is intended as an introduction to the study of stochastic processes required by Electrical Engineers in the study of communications and control systems.

Students completing this course should comprehend:

• the relationship between covariances (or correlations) and the structure of multivariate (particularly bivariate) normal distributions;

• the nature and use of stochastic transition matrices;

• the basic principles of time series analysis;

• the relationship between the time and frequency domain analysis of time series data.

Content:

Multivariate random variables. The multivariate normal distribution. Law of large numbers and the central limit theorem. Introduction to stochastic processes and Markov processes. Concepts of stationary non-stationarity as applied to these. Basic discrete time series concepts and tools. Autocovariances, autocorrelation coefficients and both time domain and power spectral representations of time series. Wiener-Khinchine theorem. Power spectra. Impulse response functions (transforms) and the concolution of these to obtain network transfer functions. A basic understanding of both transfer function analysis and spectral analysis of some of the simpler linear networks.

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