Applications of an advanced differential equation in the study of wavelets

A new wavelet family K ( t ) is discussed which represents a natural range of continuous pulse waveforms, deriving from the theory of multiplicatively advanced/delayed differential equations. K satisfies: all moments of K vanish; the Fourier transform of K relates to the Jacobi theta function; and K...

Full description

Saved in:
Bibliographic Details
Published in:Applied and computational harmonic analysis 2009-07, Vol.27 (1), p.2-11
Main Authors: Pravica, D.W., Randriampiry, N., Spurr, M.J.
Format: Article
Language:English
Subjects:
Advanced/delayed differential equation
Frame
Jacobi theta function
Pulse wavelet
Vanishing moments
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A new wavelet family K ( t ) is discussed which represents a natural range of continuous pulse waveforms, deriving from the theory of multiplicatively advanced/delayed differential equations. K satisfies: all moments of K vanish; the Fourier transform of K relates to the Jacobi theta function; and K generates a wavelet frame for L 2 ( R ) . Estimates on the frame bounds as well as the translation parameter are provided.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2008.09.002