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ECEN 5642 - Modern Methods of Spectral Estimation


Catalog Data ECEN 5642 (3). Modern Methods of Spectral Estimation. 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.
Credits and Design 3 credit hours. Elective course.
Prerequisite(s) ECEN 5612, Noise and Random Processes
ECEN 5632, Theory and Application of Digital Filtering
Textbook None.
  
Course Objectives Develop methods for modelling and analyzing signals.
Topics Covered
  1. Fourier transforms.
  2. Linear and quadratic forms in normal random variables.
  3. Quadratic estimators of the power spectrum.
  4. AR and MEM estimators of the power spectrum.
  5. Modal analysis and linear prediction.
  6. Wavelets.

Last revised: 08-02-11, PM, ARP.