Course Notes

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Course Notes for ECE 3075, Random Signals

Fall 2008

I. Basic Probability

Notes 1, review of basic probability

Notes 2, axiomatic probability

Notes 3, conditional probability

Notes 4, combinatorics

Notes 5, Bernoulli trials

II. Random Variables

Notes 6, introduction to random variables

Notes 7, moments of random variables

Notes 8, exercises using expectation

Notes 9, conditional probability

Notes 10, Gaussian and Rayleigh random variables

Notes 11, waiting in discrete/continuous time: Geometic/Exponential, Binomial/Poisson

III. Multiple Random Variables

Notes 12, introduction to multiple random variables, joint pmf/cdf/pdf

Notes 13, conditional probability and conditional expectation

Notes 14, independence and correlation

Notes 15, the moment generating function and summing two independent rv

Notes 16, the central limit theorem

Notes 17, functions of multiple random variables

IV. Basic Concepts in Statistics

Notes 18, introduction to statistical estimation, the sample mean and variance

Notes 19, the maximum likelihood estimator (MLE)

Notes 20, the maximum a posteriori estimator (MAP)

Notes 21, hypothesis testing

Notes 22, curve fitting and linear regression

V. Random Vectors

Notes 23, the covariance matrix and Gaussian random vectors

Notes 24, optimal prediction

Notes 25, linear prediction, estimating the covariance matrix, and geometry of cov matrix

VI. Random Processes

Notes 26, random process taxonomy

Notes 27, more on the autocorrelation function

Notes 28, estimating the ACF, review of LTI systems

Notes 29, WSS processes and LTI systems

Notes 30, spectral density

Notes 31, spectral density and power, removing noise by filtering

Notes 32, quantization, noise shaping

Notes 33, the matched filter

Notes 34, linear prediction

Notes 35, Poisson processes I

Notes 36, Poisson processes II, shot noise