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Linear Algebra and Adaptive Filters (Fall 2008) |
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| Course code : | ELAAF-U01 | ||
| ECTS Credits : | 7,5 | Status : | Optional |
| Placement : | 5-7 semester | Hours per week : | 4 |
| Length : | 1 semester | Teaching Language : | Not chosen |
| Principal Content : | - -Basic matrix concepts, the four related vector spaces, rank. - Vector spaces, linear combinations, linear dependence and independence, orthogonal projections, vector norms, orthogonalization. - Square systems of linear equations, Gauss elimination, partial pivoting, LU- and Cholesky factorizations. - The SVD (Singular Values Decomposition) of a matrix and it’s applications - Overdetermined systems, normal equations and least squares solution. - Eigenvalues- and vectors, diagonalization, quadratic forms, SVD. - Multivariable functions, partial derivatives, gradients, directional derivatives, Taylor approximations, quadratic forms, deterministic optimization techniques (briefly). - Random signals and their statistics, Wiener filters, linear prediction, LMS (least mean sqares) adaptive filters, RMS (recursive least mean squares) adaptive filters. Time allocation approximately: (Pure) linear algebra 60%, adaptive filters 40%. |
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| Teaching method : | Classroom lectures. Projects and group work on the basis of exercises, assignments and projects using MATLAB on a PC. | ||
| Required prequisites : | DSM2 (MAT2), a knowledge of probability theory and random signals on an introductory level, solid experience in the use of MATLAB | ||
| Responsible teacher : | Hans Pedersen
, hchpe@dtu.dk |
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