 
Summary: Multiwavelet frames in signal space originated from Hermite splines
Amir Z. Averbuch
, Valery A. Zheludev, and Tamir Cohen
{amir1,zhel,tamircoh}@post.tau.ac.il
School of Computer Science
Tel Aviv University
Tel Aviv 69978,Israel
Abstract
We present new multiwavelet frames for manipulation of discrete signals. The transforms
are implemented in two phases: 1. Pre (post)processing which transforms the scalar signal into
a vector signal (and back). 2. Transforms of the vector signal by multifilter banks. We use the
cubic Hermite splines as a source for design of interpolatory multifilter banks, which generate
frames in signal space. We use original preprocessing algorithms, which transform scalar signals
into vector arrays that serve as inputs to the oversampled analysis multifilter banks. This pre
processing algorithms do not degrade the approximation accuracy of the transforms the vectors
by multifilter banks. The postprocessing algorithms convert the vector output of the synthesis
multifilter banks into scalar signal. The discrete framelets, generated by the designed filter
banks, are symmetric and have short support. The analysis framelets have four vanishing
moments, whereas the synthesis framelets converge to Hermite splines supported on the interval
[1,1].
