ELEC 321  /  STAT 321    OUTLINE

                 Stochastic Signals and Systems

			
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                     Part I


Taught by Ruben Zamar, Statistics Department

ESB 3134,  ruben@stat.ubc.ca
                     



* Probability: Basic axioms, definitions. Conditional probability

* Random variables and vectors:  Bernoulli, binomial, Poisson, 
      normal, exponential, multivariate normal
      Statistics of random variables: expectations, second order
      statistics, higher order moments

* Uncorrelated and independent random variables

* Functions of random variables and vectors - scalar and vector valued functions

* Conditional densities, Bayes rule

* Limit theorems:  LLN and CLT -  basic understanding of convergence
  in probability and convergence in distribution

* Hypothesis testing and confidence intervals

  Assessment for Part 1: 
  2 assignments (5%+5%) + midterm test (1 hour exam) (30%) + final exam (10%)


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                    Part II  

Taught by  Lutz Lampe, EECE  

*  Stochastic Simulation

    Example: modern digital comm system

    Simulation of rv
    Inverse transform Method
    Acceptance Rejection Method
    Simulation of Gaussian rv
    Composition method : example simulating a predictor for stock 
    market or target


* Discrete valued random processes:  IID processes

Limit theorems in electrical engineering:
   Case study: central limit theorem and log normal shadowing in
   mobile wireless channels
   Law of large numbers and Shannon’s source coding theorem

* Basic information theory: entropy, Source coding: how to compress
  information, Example: Huffman Coders, MPEG video coding,

* Markov chains: Defn, basic properties,  irreducibility, recurrence,.
  Markov chains for modelling: maneuvering targets, social networks
  diffusion of information, speech recognition

* Continuous-valued Stochastic Processes
  Statistics, Stationarity, Spectral density, white Gaussian noise
  Example linear predictive coding of speech


*  Linear Difference Equations and elementary system identification
   Least Squares inference, unbiasedness and mean square consistency 
   of stochastic least squares

  Examples: Channel equalization,  deconvolution,


*Assessment for Part 2: 
2 assignments (5%+5%) + final exam (40%)