Robert Scholtz

1. Linear Algebra, matrix theory, linear spaces, bases, eigenvectors, eigenvalues, etc. (EE 441 or pass placement exam).
2. Probability theory and random variables, moments, transformations of random variables, characteristic functions and moment generating functions, etc. (EE 464 or pass placement exam).
3. Fourier, Laplace, and z transforms, complex variables, contour integrals, and residue theory (EE 401 or equivalent).

1. Supplemental course notes available on DEN website, cover primarily first half of course.
2. Recommended (but not required): Henry Stark and John W. Woods, Probability and Random Processes, Prentice Hall, 2002.
Topics:
This is a first course in random processes for engineers, and is a prerequisite for many courses in communications, controls and signal processing.
1. Definition of random processes: random variables, random vectors, random sequences, random waveforms, etc.
2. Second order statistics: Properties of correlation functions.
3. Covariance matrix factorization, eigenvalues, eigevectors, causal factoring and whitening concepts.
4. Simple hypothesis tests.
5. Linear minimum mean square error estimation, orthogonality principle.
6. Gaussian processes.
7. Linear operations, convergence concepts: convolution, integration, differentiation.
8. Time averages, stationarity, ergodicity.
9. Frequency domain analysis: time invariant linear operations.
10. Energy spectra, power spectra, white noise approximations.
11. Linear transformations of wide-sense stationary random
processes, spectral factorization, and applications.
12. Karhuenen-Loeve expansions on finite intervals.
13. Time permitting: Poisson distributed events in time, Campbell’s theorem; narrowband representations.