Rational-dilation wavelet transform with translation invariance

摘要

We propose a wavelet transform which offers a tunable Q-factor in each decomposition level and retains the translation-invariant property as well. Rational-dilation wavelet transform, whose Q-factor could be tuned before decomposition, has a finer time-frequency localization ability than common dyadic wavelet transform. However, the fixing of its Q-factor in every decomposition level restricts the freedom of frequency-domain partition, and also the up-sampler and down-sampler in its decomposition destroys translation-invariant property. We firstly analyze the decomposition and reconstruction of a kind of rational-dilation wavelet transform, and then discuss a transform that provides a tunable Q-factor in each decomposition level and keeps the translation-invariant property. Also, this method is expanded to two-dimensional case. Finally, we show the advantages of the method in time-frequency localization via the application in DEM generalization.