ECE Course Outline


Random Processes (3-0-3)

ECE 3075
Catalog Description
To develop the theoretical framework for the processing of random signals and data.
Papoulis, Pillai, Probability, Random Variables, and Stochastic Processes (4th edition), McGraw Hill, 2002. ISBN 9780072817256 (required) (comment: Book also published under ISBN: 9780073660110)

Topical Outline
Review of Probability and Random Variables
  Axioms and Properties of Probability
  Conditional Probability, Independence
  Random Variables, Density Functions, Expectation
  Moments, Normal (Gaussian) Random Variables
Two Random Variables
  Joint Density and Computation of Probability
  Independence, Correlation
  Linear Mean Square Estimation
Random Sequences
  Conditional Densities, Chapman-Kolmogorov Equation
  Normal Sequences, Sample Mean
    Markov and Chebychev Inequalities
    Convergence of Sequences, Laws of Large Numbers, Central Limit
Random Processes
  Definition, Mean, Autocorrelation, Autocovariance
  Examples: Random Phase Sinusoid, Poisson Process, Telegraph Signal,
     Random Walk, Wiener Process
  Strict Sense, Wide Sense, Stationary Increments, Cyclostationarity
  Properties of Auto- and Cross-correlation Functions
Power Spectral Density
  Definition, Relation to Fourier Transform
  Discrete-Time vs Continuous-Time
  White Noise, Spectral Estimation
Response of Linear Systems to Random Inputs
  Time Doman Analysis
  Mean and Autocorrelation of Output, Crosscorrelation of Input with Output
  Frequency Domain Analysis
  Bandpass Signals and Filters
  Shot Noise, ARMA Models
  Mean Ergodicity, Generally and for Wide Sense Stationary RP's
  Correlation and Distribution Ergodicity
Expansions of Random Processes
Markov Processes
  General Definition
  Poisson Revisited
  Discrete-Time, Discrete-State; Homogeneity, Reducibility, Recurrence
  Continuous-Time, Discrete-State; Diffusion Equations
Simulation of Random Processes
Mean Square Estimation
  Orthogonality Principle for N Observations, Whitening
  Linear and Nonlinear Estimation
  Rank Reduction
  Continuous-Time Observations, Wiener Filter