HOFSTRA UNIVERSITY Prof. Hausman
ENGG 189: RANDOM SIGNAL ANALYSIS
Course Text: PROBABILISTIC METHODS OF SIGNALS AND SYSTEM ANALYSIS, 3rd Ed. 1999
by. G.R.Cooper and C.G. McGillem (Required Text), Oxford University Press
Course Outline
Topic Sections
INTRODUCTION TO PROBABILITY 1-1 to 1-8
Random events, experiments, relative frequency approach, sets
axiomatic approach, conditional probability and independence
RANDOM VARIABLES 2-1 to 2-8
Concept of a R.V., distribution functions, density functions, mean
values and moments. Gaussian R.V. and related density functions,
other PDF’s, conditional probability functions
SEVERAL RANDOM VARIABLES 3-1 to 3-6
Two random variables, conditional probability-revisited, statistical
independence, correlation between R.V.’s, density functions for 2 R.V.’s
RANDOM PROCESSES 5-1 to 5-7
Introduction to random processes; continuous and discrete,
classifications of random processes
CORRELATION FUNCTIONS 6-1 to 6-8
Autocorrelation functions (ACF); definitions, measurements and
examples. Cross-correlation functions; definitions and properties.
SPECTRAL DENSITY 7-1 to 7-8
Introduction to Spectral Density(SD) and its relation to the Fourier
transform. Properties, and derivations of mean square values.
Relation to the autocorrelation function. White noise. Cross-spectral
density.
RESPONSE OF LINEAR SYSTEMS TO RANDOM INPUTS 8-1 to 8-9
Time domain analysis, mean and mean-square value of system
output. ACF of system output, Cross-correlation between input and output.
Analysis in the frequency domain. SD at the output. Cross spectral density
between input and output.
Reference: "Probability, Random Variables, and Random Signal Principles, 4th Ed.” By
Peyton Z. Peebles, McGraw-Hill, 2001

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