ECE 533 Random Signals and Process
Course description in catalog
Provides the foundation needed to work with the random signals which are encountered in engineering. Concept of a random variable. Properties of one- and multi-dimensional random variables. Concept of a stochastic process. Characterization of random waveforms using power spectral density and the correlation function. Random signals in linear systems. Applications to engineering systems.
Topics covered
Probability theory:
set definition, operations; joint and conditional
probability; independent events; Bernoulli trials.
Random variable:
definition; continuous, discrete, mixed random
variables; distribution function; density function;
Gaussian random variable; Binomial, Poisson, uniform,
exponential, Rayleigh random variables; conditional
distribution, conditional density function.
Functions of random variables: Y=g(X), Z=g(X,Y); determining their pdf's.
Introduction to estimation:
expectation; moment; Chebyshev and Schwarz Inequalities;
estimator for the mean and variance of the normal law.
Random vectors and parameter estimation:
definition; joint distribution and densities;
expectation vectors and covariance matrices;
multidimensional Gaussian law; characteristic functions of
random vectors; estimation of vector means and
covariance matrices; maximum likelihood estimators;
Random process:
basic definitions; important random processes; linear systems
with random inputs; wide-sense
stationarity; n-order and strict-sense stationarity; time
average and ergodicity; Karhunen-Loeve Expansion.
Applications to statistical signal processing:
Orthogonality and linear estimation; Kalman filtering; Expectation-Maximization algorithm; simulated annealing.