ECE 430 Random Signal Analysis, Spring 1996

1/23	Distribute syllabus.  Introductory lecture.  Survey:
        WSS processes through LTI systems, PSDs.  Wiener
        filter, matched filter.  Markov chains, queuing
        model, stationary distribution.  Probability on
        the set {1,...,N}, probability on the set
        { (b_1, b_2, b_3): b_i = 0 or 1 } with the
        binomial(\theta) distribution.  Probability densities
        on [0,\infty), as a model of lightbulb lifetime.

1/25    Worked problems 2.1, 2.2, 2.5 from text.
	Discussed axioms of probability.
        Assigned HW 2.4, 2.15, 2.17, 2.24 DUE Thur. 2/1.

1/30	More properties of probability.  Modeling example from
	optical communications.  Section 2.4 conditional
	probability.  Law of Total Probability, Bayes' Rule.

2/1	Binary symmetric channel (BSC) example.  Independent
	events.  Section 3.1, random variables and Section 3.2,
	cumulative distribution functions (cdfs).
	Assigned HW 2.56, 2.57, 2.59, 2.62, 2.63, 2.64
	DUE Thurs. 2/8.

2/6	Section 3.2, more discussion of cdfs.  Discrete and
	continuous RVs, pmfs.  Section 3.3, pdfs.

2/8	More on pdfs and pmfs.  Section 3.4, important pdfs and pmfs.
	Assigned HW 3.1, 3.6, 3.16, 3.17, 3.19,
	3.20(c), 3.21(c), 3.23 DUE Thurs. 2/15.

2/13	Delta functions and mixed RVs.  Conditional cdfs, pdfs.
	Section 3.5, functions of RVs.

2/15    Examples illustrating the material in Section 3.5.
        Assigned HW Handout, also
        3.52, 3.59, 3.62, 3.58 DUE Thurs. 2/22.

2/20    More examples for Section 3.5.

2/22	Section 3.6 Expectation for discrete and continuous RVs.
	Expectation for functions of RVs.
	Assigned HW 3.71, 3.76, 3.78 DUE Thurs. 2/29.

2/27	More examples from Section 3.6:  2nd moments and variance.
	Section 3.7:  Markov's inequality, Chebyshev's inequality.
	Skip Section 3.8.  Section 3.9:  Transform methods.

2/29	Yes, this is a leap year!
	More on transform methods from Section 3.9.  The Chernoff bound.
	Assigned HW 3.89, 3.91 and HANDOUT DUE Thur. 3/7.

3/5	Chapter 4.  Cdfs and pdf of random vectors.
	Computing probabilities.

3/7	Independent RVs, expectations of; linearity of expectation.
	NO HW assigned.

3/12	No class - Spring Recess
3/14	No class - Spring Recess

3/19	Conditional pmfs and pdfs.  Laws of Total Probability.
	The substitution principle.  Indpendence property.
	Applications and examples.

3/20	No OH; exam review 2:30-3:30 in 3359 EH

3/21	Mid-term exam
	Assigned HW 4.3, 4.10, 4.11, 4.13, 4.17, 4.25, 4.37(a),
	4.38(a)(b)(c) DUE Thur. 3/28.

3/26	Another example using material from 3/19.  Mixed RVs.

3/28	Comm. channel example.  Conditional expectation.  Laws of
	total prob., substitution principle, independence property.
	Bivariate Gaussian RVs.
	NO HW assigned.

4/2	Section 4.9 Minimum mean-square error estimation and conditional
	expectation; the orthogonality principle.  Linear (affine)
	minimum mean-square error estimation; another orthogonality
	principle.  Chapter 6 Random Processes.  The mean function,
	the (auto)correlation, and (auto)covariance functions.
	Assigned HW 4.48, 4.50, 4.60, 4.37(b), 4.82
        DUE Thur. 4/11.

4/4	Definition of stationary random process and wide-sense
	stationary (WSS) random process.  Properties of the
	correlation function R(t) of a WSS process.  WSS processes
	through LTI systems.  If the input is WSS, so is the output.
	Average power in a WSS process.  Power spectral density.
	Assigned HW 6.53, 6.56(a), 6.63(a) DUE Thur. 4/11.

4/9	WSS processes through LTI systems.  Joint WSS.  Relationships
	between the input and output power spectral densities and
	cross power spectral densities.
	Assigned HW 7.1(b) also sketch S_X(f), 7.2, 7.3, 7.7,
	7.19, 7.21 DUE Thur. 4/18.

4/11	Derivation of the matched filter.  Derivation of the Wiener filter.

4/16	The Poisson Process.
	Assigned HW 6.31, 6.35, 6.36, 6.37 DUE Thur. 4/25.

4/18	The smoothing property of conditional expectation.  Continuous-
	time Markov chains with stationary transition probabilities.
	The Chapman-Kolmogorov equation.
	Also Poisson process handout.

4/23	Birth and death processes.  The Kolmogorov's backward and forward
	differential equations.  Stationary distributions.  Examples.

4/25	Discrete-time Markov chains.
	Assigned HW Problems written on blackboard DUE Thur. 5/2.

4/30	Worked several examples of solving for the stationary distribution
	of a discrete-time Markov chain.  Distributed a handout with
	review problems and old exams.
	Assigned HW 8.5, 8.6, 8.8, 8.10 plus handout DUE Thur. 5/9.

5/2	Presented examples of discrete-time Markov chains:  random walk,
	random walk with reflecting barrier at 0, random walk with
	absorbing barrier at 0, random walk with absorbing barriers at
	0 and at N as a model for the Gambler's ruin problem.
	Feedback systems driven by white noise.

5/7	Branching processes as Markov processes.
	Statistics and the weak law of large numbers.  The strong law
	of large numbers.  The central limit theorem.

5/9	Review for final exam.

5/12	SUNDAY 12:25. Final Exam in 104 Fred Hall