## EC458 Mathematical Algorithms for Signal Processing

### Course Name:

EC458 Mathematical Algorithms for Signal Processing

### Programme:

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### Credits (L-T-P):

### Content:

Mathematical Foundations – mathematical models, random variables and random processes, markov and hidden markov models. Represenations and approximations - orthogonality, least squares, MMSE filtering, frequency domain optimal filtering, minimum norm solutions, Iterated reweighted least squares. Linear Operators – Operator norms, adjoint and transposes, geometry of linear equations, least squares and pseudo inverses, applications to linear models. Subspace methods – Eigen decomposition, KL transform and low rank approximation, Eigen filters, signal subspace techniques – MUSIC, ESPRIT. SVD – matrix structure, pseudo inverse and SVD, system identification using SVD, Total least squares, partial total least squares. Special matrices – Toeplitz matrices, optimal predictors and lattice filters, circulant matrices, properties.