Minimally Supported Frequency (MSF) d-Dilation Wavelets

Abstract

In this paper, we provide a geometric construction of a symmetric 2n-interval minimally supported frequency (MSF) d-dilation wavelet set with d∈(1,∞) and characterize all symmetric d-dilation wavelet sets. We also provide two special kinds of symmetric d-dilation wavelet sets, one of which has 4m-intervals whereas the other has (4m+2)-intervals, for m∈N. In addition, we construct a family of d-dilation wavelet sets that has an infinite number of components.

Framelet Sets and Associated Scaling Sets

“…Weiss [14] first proposed the concept of the minimally supported frequency (MSF) wavelets which can split a signal into a set of non-overlapping frequency regions. The construction of MSF wavelets has been widely applied [15].…”