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EC 520 LINEAR ALGEBRA AND RANDOM PROCESSES 4-0-0-8

Linear Algebra: Basic analysis and topology. Vector spaces, linear operators and matrices. Decomposition theorems and eigen-analysis.Quadratic forms. Perron-Frobenius theorems.Probability: Spaces and random variables. Distributions. Transformations and moment analysis. Stochastic processes and covarianceanalysis. Estimation theory.

Texts/References:1. K. Hoffman and R. Kunze:Introduction to Linear Algebra; Prentice-Hall, 1996, 2/e.2. R. Horn and C. Johnson: Matrix Analysis; Cambridge, C.U.P.,19913. A. Papoulis: Probability, Random Variables and Stochastic Processes; McGraw-Hill, 1991, 3/e.4. H. Stark and J.W. Woods: Probability, Random Variables and Estimation Theory for Engineers; Prentice Hall, 1994.

EC 521 SIGNAL PROCESSING 3-0-0-6

Continuous-time and discrete-time signals and systems; Spectral analysis: CTFT and DTFT, DFT, FFT and STFT; Sampling, Quantization,Decimation and Interpolation; Z-transform: definition and ROC; Digital filters: FIR and IIR filters, Digital-filter realisations and design, Finitewordlength effects; Adaptive filtering: steepest-descent algorithm, LMS, variants of LMS, LS, RLS, blind algorithms.

Texts/References:1. S. Haykin, Adaptive Filter Theory, PHI, 2001. 2. A.V. Oppenheim and R.W. Schafer, Discrete- Time Signal Processing, PHI, 2000. 3. S. K. Mitra, Digital Signal Processing, TMH, 3/e, 2006. 4. S. J. Orfanidis, Introduction to Digital Signal Processing, Prentice-Hall, 1996.

EC 522 STATISTICAL SIGNAL PROCESSING 3-0-0-6

Review of signals, systems and linear algebra; Review of random variables; Review of random processes: LSI system with random inputsignal, Paley-Wiener criterion, spectral factorization theorem, Wold’s decomposition; Random signal modeling: MA, AR, ARMA models;Parameter estimation: necessary and sufficient statistic, CRLB, maximum likelihood and Bayesian estimation; Optimal linear filtering:LMMSE, WH equations, FIR and IIR Wiener filters; Linear Prediction: Yule-Walker equations, Levinson-Durbin Algorithm, lattice filter;Adaptive filtering from Wiener filtering prospective; Kalman filters; Spectral estimation: periodograms, modified periodograms, minimumvariance, maximum entropy and parametric methods for spectral estimation.

Texts/ References:

1. M. H. Hayes, Statistical Digital Signal Processing and Modeling, John Wiley & Sons, Inc., 2002.2. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall,1993.3. J. G. Proakis et. al., Algorithms for Statistical Signal Processing, Pearson Education, 2002.4. H. Stark and J. W. Woods, Probability and Random Processes with Application to Signal Processing, PHI, 2002.5. S. Haykin, Adaptive Filter Theory, PHI, 2001.

EC 523 DIGITAL SIGNAL PROCESSORS 2-0-3-7

Introduction: Computational characteristics of DSP algorithms and applications; Techniques for enhancing computational throughput: