ECE-S 632

    DREXEL UNIVERSITY

    Department of Electrical and Computer Engineering
    Winter Quarter 2001
     

    DIGITAL SIGNAL PROCESSING II ECE-S 632 - 501

    INSTRUCTOR

    • [   ] Prof. Athina Petropulu Rm. 7-221, Tel. x2358, e-mail: athina@artemis.ece.drexel.edu
      Office Hours: Monday 3-5 or by appointment

    CLASS SCHEDULE: Monday 6-9, Rm. 7-306

    PREREQUISITE:  Graduate standing, ECE-S 631, Stochastic Processes

    TEXTBOOK

    • [   ] Class Notes

    • [   ] S. Kay, Modern Spectral Estimation, Prentice Hall Inc., Englewood Cliffs, N.J. 1988.

    REFERENCES

    • [   ] S.L. Marple, Digital Spectral Analysis, Prentice-Hall, 1987.

    • [   ] C.L. Nikias and A.P. Petropulu, Higher Order Spectra Analysis, Prentice-Hall, 1993.

    • [   ] W. Gardner, Statistical Spectral Analysis: a nonprobabilistic theory, Prentice-Hall, 1988.

    • [   ] The tutorial Articles from IEEE Signal Processing Society Magazine:
      · C.L. Nikias and J. Mendel, ``Signal processing with higher order spectra," 10(3), July 1993, pp.10-37
      · W. A. Gardner, ``Exploitation of Spectral Redundancy in Cyclostationary Signals,'' April 1991, pp. 14-36.
      · F. Hlawatsh and F. Boudreaux-Bartel, ``Linear and quadratic time-frequency signal representations", 9(2), 1992, pp. 21-68
      · O. Rioul and M. Vetterli, ``Wavelets and signal processing", 8(4), 1991, pp. 14-38.

    COURSE DESCRIPTION

    • [   ] The representation of a stationary random process by its spectrum can be an efficient and revealing description of the process. Spectral analysis is used to detect periodicities in the data, and is quite powerful in signal processing tasks such as data modeling, forecasting, system identification and signal detection. The course presents various power spectrum estimation techniques, and compares them in terms of resolution, accuracy (bias) and reliability (variance). It introduces higher-order spectra as an extension of the conventional spectrum (second-order spectrum), and points out important applications. Conventional spectral analysis is implemented assuming that the underlying mechanism generating the data does not vary with time. The course also treats signals whose frequency content varies with time.

    GRADING POLICY

    • [   ] Homework: 20%

    • [   ] Projects: 80%

TENTATIVE COURSE OUTLINE

    • Introduction
      Historical perspective; Review of stochastic processes; Useful concepts in spectral analysis; Applications.

    • Conventional Spectrum Estimation
      Periodogram and Welch method; Blackman-Tukey method; Bartlett's method; Window functions.

    • Maximum Likelihood Method (MLM) of Capon

    • Maximum Entropy Method (MEM)
      Levinson Recursion; Relationship between MLM and MEM.

    • Parametric Modeling of Time Series
      AR, AM, ARMA stochastic process models; Spectral factorization.

    • AR Spectrum Estimation
      Yule-Walker method; Weighted Burg techniques; Least-squares Linear Prediction; Model order Selection Criteria.

    • ARMA Spectrum Estimation

    • Harmonic Decomposition methods
      ARMA Processes for sinusoids in white noise; Prony's method; Identification of exponentials in noise; Eigenanalysis based frequency estimators (MUSIC, Pisarenko)

    • Higher Order Spectra
      Motivation; Definition and Properties of Moments and Cumulants; Advantages; Applications.

    • Nonstationary Signal Analysis
      Wavelet transform; Time-frequency representations.