(See also Projects related to the course on Fourier analysis)
The project relates to problems which appear both in signal analysis and complex analysis. The contemporary digital techniques of dealing with signals (sound records etc.) assume that a continuous signal is replaced by a sequence of its values (samples) at consequent moments of time, this sequence of samples is transmitted or stored, and later one reconstructs the original signal from this sequence of sampled values.
Since each "realistic" signal has a bounded frequency band the problem of reconstruction of such signals from their sampled values becomes one of the central ones. It was treated in many (now) classical works in signal analysis, but a lot of questions both theoretical and applied still remain open. These problems are related to noised signals, noised sequences of points and also signals with special behavior in time or/and frequency.
On the other hand each bandlimited signal can be prolongated from the real (time) axis to a holomorphic function in the whole complex plane and thus methods of complex analysis come into the play. They proved themselves to be very efficient.
Depending upon student's interests the project can deal with mainly either numerical or theoretical problems and can be designed for a group from one to three students.
The project can include collaboration with other research groups in particular with the group of Numerical Harmonic Analysis in Vienna Technical University, Austria (NuHAG)
The project can be designed for a group from one to three students. The project can include collaboration with other research groups in particular with the group of Numerical Harmonic Analysis in Vienna Technical University, Austria (NuHAG)