ECE752 - spring 2003

SPECTRAL ESTIMATION

Professor Yariv Ephraim

STII Room 221

yephraim@gmu.edu

 

Office Hours:         Tuesday 2:00-3:00 pm (by appointment)

Thursday 2:00-3:00 pm 

 

 

Course Description: In depth study of spectral analysis and its application to statistical signal processing. This course covers classical Fourier analysis of deterministic signals, Wiener theory for spectral analysis of random processes, parametric and non-parametric approaches for estimating the power spectral density such as the classical window method, maximum entropy, signal subspace and Wavelets.

 

Course Outline:

 

  1. Fourier series and Fourier transform for deterministic and random processes.
  2. Wiener-Khintchine theory of spectral analysis.
  3. Foundations of parameter estimation theory.
  4. Discrete spectra estimation (periodogram).
  5. Continuous spectra estimation (smoothed periodogram).
  6. Maximum entropy and Autoregressive spectral estimation  (Levinson-Durbin algorithm).
  7. Signal subspace methods MUSIC and ML)
  8.  Wavelet transform and its relation to the Short Time Fourier Transform 

 

 

Text Book:

 

M. B. Priestley, Spectral Analysis and Time Series, Academic Press, London, 1989.

 

Additional References:

 

  1. David R. Brillinger, Time Series: Data Analysis and Theory. SIAM 2001.
  2. S. M. Kay, Modern Spectral Estimation-Theory and Application. Prentice-Hall, Englewood Cliffs, New Jersey, 1988.
  3. G. P. Tolstov, Fourier Series. Dover Publications, Inc., 1962.

 

Prerequisite: ECE528 or Instructor’s permission. ECE 535 is not required.

 

Grading: Three equally weighted take-home assignments.