ECEN 5642 - Modern Methods of Spectral Estimation
3 credit hours
Catalog Description:
Spectrum analysis is
comprised of techniques for analyzing speech, mechanical vibrations,
radiated fields, seismic traces, radar returns, sonar signals, and
natural time series. In this course we review the formulas of Fourier
analysis for continuous-, discrete-, and mixed-time signals. We then
develop the theory of multiwindow quadratic estimators of the power
spectrum. We study the theory of rational modelling and apply it to
the estimation of AR and MEM spectrum models. We encounter the Levinson
and Schur recursions for fitting AR models to correlation data and the QR
and Burg algorithms for fitting AR models to time series data. We then
study the many subspace methods for fitting complex exponential modes to
experimental data.This leads to a study of MUSIC and the many subspace
methods of linear prediction. Finally, we develop the transform calculus
of multirate time series and study the wavelet transform as it applies to
the estimation of time-frequency distributions.
Prerequisites:
ECEN 5612, Noise and Random Processes, and
ECEN 5632, Theory and Application of Digital
Filtering
Textbook:
None.
Goals:
Develop methods for modelling and analyzing signals.
Topics:
- Fourier transforms.
- Linear and quadratic forms in normal random variables.
- Quadratic estimators of the power spectrum.
- AR and MEM estimators of the power spectrum.
- Modal analysis and linear prediction.
- Wavelets.
Computer Usage:
- MATLAB, FORTRAN, C.
Laboratory Projects:
- Individual class
projects covering one or more topics of the course as it applies to a
practical problem.
ABET Category Content:
