EE60015: Computational Methods And Algorithms In Signal Processing

EE60015
Course name	Computational Methods And Algorithms In Signal Processing
Offered by	Electrical Engineering
Credits	4
L-T-P	3-1-0
Previous Year Grade Distribution
1 4 1 1 1 EX A B C D P F
Semester	Autumn

Syllabus

Syllabus mentioned in ERP

Random variables, vectors and random processes, Discrete-time stochastic processes, Linear systems with stationary random inputsVECTOR SPACES AND LINEAR ALGEBRA:Signal Spaces: Linear transformations: range and nullspace, Projections and orthogonal projections, Projection matrices, The projection theorem, Orthogonalization of vectors.Linear operators and matrix inverses: The LU factorization, The Cholesky factorization, Unitary matrices and the QR factorizationEigenvalues and Eigenvectors: Eigenvalues and linear systems, Linear dependence of eigenvectors, Diagonalization of a Matrix, The Gershgorin circle theorem, Eigenfilters, Moving the eigenvalues around, Noiseless constrained channel capacity, Computation of eigenvalues and eigenvectorsThe Singular Value Decomposition: Matrix structure from the SVD, Pseudo-inverses and the SVD, Numerically sensitive problems, Rank-reducing approximations: effective rankSome special matrices and their applications: Permutation matrices, Toeplitz matrices and some applications, Vandermonde matrices, Circulant matrices, Triangular matrices, Properties preserved in matrix productsLinear Signal Model:Synthesis of coloring filter and Analysis of whitening filter, Rational power spectra (AR, MA, ARMA), Relationship between filter parameters and autocorrelation sequences, Lattice-Ladder filter realizationITERATIVE AND RECURSIVE METHODS IN SIGNAL PROCESSINGBasic concepts and methods of iterative algorithms: Newton's method, Steepest descent, LMS adaptive filtering, Blind source separationIterative algorithms: Iterative methods for computing inverses of matrices, The Jacobi method, Gauss-Seidel iteration, Successive over-relaxation (SOR), Algebraic reconstruction techniques (ART), Conjugate direction methods, Conjugate gradient methodThe Expectation Maximization Algorithm: General Statement of the EM Algorithm, Hidden Markov Models, The E and M steps, The forward and backward probabilities, Discrete output densities, Gaussian output densities, Normalization, Algorithms for HMMs, Spread-Spectrum, Multi-User CommunicationMETHODS OF OPTIMIZATION:Shortest path algorithms and dynamic programming:The Viterbi algorithm, Code for the Viterbi algorithm, Related algorithms: Maximum-likelihood sequence estimation, The Intersymbol interference (ISI) channel, Code division multiple access (CDMA), Convolutional decoding, HMM likelihood analysis and HMM training, Lielikhood, Evaluation, Decoding, problem, Dynamic warping.

Time Table

Day	8:00-8:55 am	9:00-9:55 am	10:00-10:55 am	11:00-11:55 am	12:00-12:55 pm		2:00-2:55 pm	3:00-3:55 pm	4:00-4:55 pm	5:00-5:55 pm
Monday										NEX201
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