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Linear Algebra and Adaptive Filters (Spring 2007) |
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| Course code : | ELAAF-U01 | ||
| ECTS Credits : | 7,5 | Status : | Optional |
| Revised : | 06/12 2004 | Written : | 15/03 2002 |
| Placement : | 5-7 semester | Hours per week : | 4 |
| Length : | 1 semester | Teaching Language : | English if English students are present |
| Objective : | To introduce basic concepts of linear algebra and adaptive filters. Combining the two main topics will allow the demonstration of how linear algebra provides the theoretical foundation and computational tools for an important technical field. Therefore, the course will focus equally on theory and on practical applications. The students will be required to make extensive use of related software as well as develop their own. | ||
| Principal Content : | - Basic matrix concepts, the four related vector spaces, rank, condition number, norm. - Vector spaces, linear dependence and independence, orthogonal projections, vector norms, orthogonalization. - Square systems of linear equations, Gauss elimination, partial pivoting, LU- and Cholesky factorizations, error analysis. - Overdetermined systems, normal equations and least squares solution, QR-factorization. - Eigenvalues- and vectors, diagonalization, transformations of the eigenspectrum, the power method and inverse iteration. - Taylor approximation in the n-dimensional case, quadratic forms, optimization techniques (briefly). - 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%. | ||
| Teaching method : | Lectures, classroom exercises and computerlabs, computerbased assignments. Group work. | ||
| Required prequisites : | Documented knowledge corresponding to DSM3/DSM4 | ||
| Recommended prerequisites : | - Solid experience in the use of Matlab. | ||
| Relations : | - | ||
| Type of examination : | Oral examination based on assignments | ||
| External examiner : | Internal | ||
| Marking : | Scale of 13 | ||
| Remarks : | During the semester two obligatory assignments are given. In both cases students are expected to work in groups, and in both cases the assignment will require the analysis of a given problem, use of Matlab to develop a tool for solution, followed by experiments and an analysis thereof. The work must be described in a report. The oral examination at the end of the semester will include a student-presentation of material covered in both assignments, followed by questions from the examiner: At the examination each student is allocated 20 minutes. The examination is a group examination, but the marking is individual. The evaluation is based on the quality of the two assignment-reports and the oral per-formance. At the examination the group initially presents the main structure of both projects in writing. Each student will then individually present a part of one of the two projects. The part in question is picked at random. The student is allowed the use of material (overheads, software) prepared by the group collectively. The duration of the presentation is 12 minutes, allowing 8 minutes for subsequent questions from examiner and censor. These questions may be adressed to the student or the group. After the examination of the last group member, the group leaves the room whil the evaluation is in progress. Afterwards the group is summoned, and the individual marks are given and explained. | ||
| Teaching material : | HCP: Notes. | ||
| Responsible teacher : | Hans Pedersen
, hchpe@dtu.dk |
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