Fall Term, 2001.
Professor: Dr. S. Ferrando. Office: S241L
Time and Location: Wednesday T216A, 11:10-2:00.
Office hours will be announced in class.
Evaluation:
There will be 2 assignments each worth 30%. They will be based on
a set of exercises distributed in class. These assignments
will consist of standard
problems plus questions that have to be answered by the use of a
computer. There will be a final exam worth the remaining 40%.
The content, time and location of this exam will be announced in class.
Material to be covered:
1. Estimation in signal processing. Assesing estimation performance. Minimum variance unbiased estimation. Overview of estimation procedures: CRLB, Linear Models, Maximum Likelihood, Least Squares, Method of Moments and Bayesian estimators.
2. Cramer-Rao Lower Bound (CRLB). Transformation of parameters, vector parameter. CRLB for the general Gaussian case. Signal processing examples.
3. Basic concepts in spectral estimation. Properties of power spectral densities. The spectral estimation problem.
4. Nonparametric methods. Periodogram and correlogram methods. Periodogram computation via FFT. Bias analysis of the periodogram. The Blackman-Tuckey espectral estimate. Window design considerations. Other refined periodogram methods.
5. Parametric methods for rational espectra. Covariance structure of ARMA processes. Yule-Walker method. Least squares method. Multivariate ARMA signals.
6. Filter bank methods. Filter bank interpretation of the periodogram. Refined filter bank method (RFB). Capon method and its relation with AR methods. Filter bank interpretation of the periodogram.
7. Spatial methods. Array model. The modulation-transmission-demodulation process. Model equation. Beamforming. Capon method.
Textbook:
Introduction to Spectral Analysis by P. Stoica and R. Moses. Prentice Hall 1997. Availabale at Ryerson's bookstore.
Useful Books:
Fundamentals of Statistical Signal Processing,
Vol. 1, S. Kay. Prentice Hall, 1993.
Introduction to Time Series and Forecasting,
P. Brockwell, R. Davis. Springer, 1996.
More Advanced Books:
Statistical Signal Processing Detection, Estimation and Time Series
Analysis, L. Scharf. Addison-Wesley, 1991.
The Spectral Analysis of Time Series, L. Koopmans. Academic
Press 1974.