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.