On time-frequency analysis and time-limitedness
P.J. Oonincx · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1997
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. 1991 Mathematics Subject Classification: 33C55, 44A15, 45C05, 62M15, 94A12. Keywords and Phrases: Wavelets, tapers, prolate spheroidal wave functions, Wigner-Ville distribution, spectral analysis, truncation problem. Note: Work carried out under project PNA 4.2 "Wavelets" and supported financially by the Technology Foundation (STW), project...