On time-frequency analysis and time-limitedness
We study two classical problems, namely the concentration of energy problem and the truncation problem. The first problem deals with time-limited signals that have maximal energy in a certain frequency band. The second problem is about estimating the spectrum of a signal, if this signal is only known at a certain interval. Solutions of the first problem can be used to obtain good solutions for the second one by means of a preprocessing algorithm, called tapering. The truncation problem and the tapering algorithm are also studied for time-scale and time-frequency analysis, using the continuous wavelet transform and the Wigner-Ville representation.
|Spherical harmonics (msc 33C55), Special transforms (Legendre, Hilbert, etc.) (msc 44A15), Eigenvalue problems (msc 45C05), Spectral analysis (msc 62M15), Signal theory (characterization, reconstruction, filtering, etc.) (msc 94A12)|
|CWI. Probability, Networks and Algorithms [PNA]|
Oonincx, P.J. (1997). On time-frequency analysis and time-limitedness. CWI. Probability, Networks and Algorithms [PNA]. CWI.