An advanced introduction to the processing and modeling of random discrete-time signals. Random time series, auto- and cross-correlation sequences and their generation, filtering of random sequences, Wiener filter, matched filters, modeling assumption errors, one-step predictors, rational modeling of random sequences, parametric and non-parametric spectral estimation.
Digital signal processing algorithms find application in a large variety of situations. Many of these applications deal with signals about which there is a degree of uncertainty, so that digital signal processing has to be combined with probabilistic aspects for discrete time stochastic processes. Digital signal processing algorithms for random sequences are designed on the basis of spectral knowledge that most often has to be arrived at by estimation. The parametric and non-parametric estimators become an important aspect of the design process.
The prerequisite material consists of the basic tools for characterizing and processing random signals, as covered in ECE 5605, and the basic tools for deterministic digital signal processing and their application to digital filter design and Discrete Fourier analysis, as treated in ECE 4624.
Percentage of Course
|1. Random time series, correlation, spectral density||10%|
|2. Linear system response characterization, spectral factorization, whitening||15%|
|3. Covariance generation for ARMA systems and its applications||10%|
|4. Matched and Wiener filtering, orthogonality, smoothing, prediction, one-step prediction||10%|
|5. Fast algorithms: Durbin and Levinson recursions||10%|
|6. Periodogram, resolution, MA estimation, correlation, smoothed and averaged periodogram, Barlett/Welch||15%|
|7. Rational modeling: AR and ARMA, ladder structures, reflection coefficients, maximum entropy||15%|
|8. Model choice, order estimation||5%|
|9. Covariance sequence/matrix parameterization and its applications||10%|