The high frequency behaviour of continuous wavelet transforms

Abstract

The high frequency behaviour of continuous wavelet transforms is characterized by the number of vanishing moments of the corresponding basic wavelets. As a consequence we give satisfying answers to the following questions of theoretical as well as practical interest:

What are the differences or similarities between transforms to different wavelets?

Why do wavelet transforms react so sensitively to abrupt signal changes ?

Keywords:

• Wavelet transform
• high frequency behaviour
• decay rate