University of Toronto
Department of Electrical & Computer Engineering
Communications Group

ECE 1514S, Spring 1998

• Instructor: Prof. D. Hatzinakos
• Office: Galbraith Building, Room 447
• Telephone: 978-1613
• E-Mail: dimitris@comm.toronto.edu

Main References:

1. Class notes (from Copy Centre, SF B540) D. Hatzinakos, Spectral analysis and Array Processing -- Class notes available at Copy Centre, SF B540.
2. S.M. Kay, Modern Spectral Estimation , Prentice-Hall Inc., 1988

Lectures:

Friday 11:00 - 13:00 p.m., GB404

(starting January 9, 1996)

Composition of Final Mark:

Project 1:   30%  (to be assigned: Jan. 16,   due: Feb.  27)
Project 2:   30%  (to be assigned: Feb. 27,   due: April 3)
Final Exam:  40%  Friday April 10, during  lecture time

Topics Covered Will Include

                                                                    page
I.   INTRODUCTION                                                      1
     Historical perspective                                            2
     Definitions of Power Spectrum: Deterministic and Stochastic      10
     Useful concepts and issues in spectral analysis                  16
     Applications                                                     23

II.  CONVENTIONAL POWER SPECTRUM ESTIMATION                           27
     Periodogram and Welch method; window functions                   28
     Autocorrelation method of Blackman-Tukey and Barlett method      39
     Properties                                                       45
     Examples                                                         46

III. MAXIMUM LIKELIHOOD METHOD (MLM) OF CAPON                         52
     Derivation; Properties; Modifications

IV.  MAXIMUM ENTROPY METHOD (MEM)                                     59
     Maximum entropy principle                                        59
     Levinson Recursion                                               62
     Relationship between MLM and MEM                                 66
     Performance comparisons between CONV, MLM and MEM                68

V.   PARAMETRIC MODELING OF TIME SERIES                               75
     AR, MA and ARMA Stochastic process models                        78
     Relationship of AR, MA and ARMA parameters                       80
     Spectral factorization                                           92

VI.  AUTOREGRESSIVE (AR) POWER SPECTRUM ESTIMATION                    94
     Yule-Walker (YW) method                                         101
     Least-squares  linear  prediction  techniques  (Covariance,  
     Modified  Covariance, CLS)                                      103
     Weighted Burg techniques                                        108
     Model order selection criteria                                  112
     Performance comparisons                                         116

VII. MOVING AVERAGE (MA) SPECTRUM ESTIMATION                         122
     Nonlinear optimization Method                                   124
     Durbin's Method                                                 125

VIII.ARMA POWER SPECTRUM ESTIMATION                                  129
     The optimum ARMA method;                                        130
     The Modified YW Method;                                         131
     The Modified Levinson Recursion Algorithm                       133
     Least Squares Modified YW Methods                               135
     Model order selection criteria                                  141

IX.  HARMONIC DECOMPOSITION METHODS                                  147
     Singular Value decomposition (SVD)                              147
     Modelling sinusoids in white noise                              154
     Original Prony method                                           157
     Least-squares Prony method                                      161
     Eigenanalysis based frequency estimators                        170
     Signal subspace methods and noise subspace methods              171

X.   SPECTRAL ANALYSIS OF NONSTATIONARY SIGNALS                    180(a)
     Methods for locally stationary signals                          181
     Adaptive Power Spectral Analysis                                187
     Wavelets                                                     191(1)
     Cyclostationary Spectral analysis                           191(10)

XI.  ARRAY SIGNAL PROCESSING                                      192(a)
     Introduction to array processing systems                     192(b)
     Array Processing methods                                        202
     Signal subspace and noise subspace array processing method      214
     Resolving coherent sources                                      226
     Adaptive beam forming                                           238

XII. MULTICHANNEL SPECTRAL ESTIMATION                                251
     Multichannel concepts                                           252
     Conventional estimators                                         260
     Multichannel minimum variance spactral estimation               264
     Parametric estimators                                           265

XIII.MULTIDIMENSIONAL SPECTRAL ESTIMATION                            277
     Conventional Estimation methods                                 289
     AR Estimation methods                                           293

XIV. HIGHER-ORDER SPECTRAL ANALYSIS                                  301
     Definitions and properties of bispectrum and trispectrum        310
     Conventional Estimators                                         327
     Parametric Methods (MA, AR, ARMA)                               342
     Cepstrum Approaches                                             363

     References                                                      373