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TMA 4170 Fourier analysis
Høst, 2005
I can offer a number of projects on mathematical problems which are motivated by needs of signal analysis. Currently these problems are in the scope of my research interests, so the level of difficulty can vary substantially: from some survey projects, to ones containing "real" interesting problems. It is also possible to have projects related to numerical simulation.
I maintain collaboration with researches groups in signal analysis in Europe and USA, so successful projects may yield further international cooperation.
Here is the list of topics in which I can offer projects
This is a classical area of research, (we shall discuss it later
in the course) still a lot of important problems
remain open. They concern signals with lacunar spectra,
multidimensional
signals
and also signals with nonuniform behavior in the time domain.
This is a respectively new area related to development of digital techniques. The way to store and/or transmit a signal is to quantize it, i.e. transform into a sequence of bits, and then (when need be) reconstruct this sequence into a signal which is close to the original one. Problems of economical and robust quantizing are of great importance, on the other hand they are related to various basic mathematical disciplines, from Fourier Analysis to Abstract Algebra.
Well, I spoke a lot about this matter
during the lectures. I am especially interested in systems of vectors which
possess some symmetry both in time and in frequency domains.
In particular functions with double orthogonality (we shall discuss
them in the course fo rthe continuous case)
Their continuous analogs are well-known and enjoy interesting and important
properties.