Some scale-time localization properties of the continuous wavelet transform

Abstract

Time-Frequency localization or concentration principles are fundamental concepts of signal processing and related fields. We shall prove some simultaneous localization or concentration inequalities for the ContinuousWavelet Transform. We will also show that simultaneous localization in the scale-time(space) is impossible, in the sense that the scale sections of the support of the wavelet transform of a non null Lp-function can not have finite Lebesgue measure.