The BRADLEY DEPARTMENT of ELECTRICAL and COMPUTER ENGINEERING

# ECE 6624 Spectral Estimation & Modeling | ECE | Virginia Tech

### Course Information

#### Description

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.

#### Why take this course?

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.

### Learning Objectives

• Characterize signals in terms of spectral models
• Design optimal filters, such as Wiener and matched filters, from given information
• Recognize which spectral information is needed for a given application, and derive estimates for that information from data records
• Contrast parametric and non-parametric spectral estimation methods
• Apply spectral modeling techniques and evaluate their appropriateness for the observed data

### Course Topics

#### 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%