DocumentCode :
2620814
Title :
On orthogonal wavelets with oversampling property
Author :
Xia, Xiang-Gen ; Zhang, Zhen
Author_Institution :
Dept. of Electr. Eng. Syst., Univ. of Southern California, Los Angeles, CA, USA
fYear :
1994
fDate :
27 Jun-1 Jul 1994
Firstpage :
130
Abstract :
Considers the orthogonal scaling functions with the following general oversampling property: for a fixed integer J⩾0 and any f∈V0, f(t)=Σnf(n/(2J))φ(2Jt-n). The authors call that an orthogonal scaling function φ(t) satisfying the above equation has the oversampling property with sampling rate 2-J and denote all such scaling functions by SJ. Thus, S 0 consists of all orthogonal scaling functions with the sampling property and SJ ⊂SJ+1 for J=0, 1, 2, …. The results in Walter (1993) also show that S0≠S 1, i.e., the space of the orthogonal scaling functions with the sampling property is a proper subspace of the one of the orthogonal scaling functions with the oversampling property. Let Se and Sc denote all orthogonal scaling functions with exponential decay and compact support, respectively. The present authors prove that S0∩Se=SJ∩Se and S 0∩Sc=SJ∩Sc={the Haar function} for any J⩾O. In another words, if an orthogonal scaling function with exponential decay has the oversampling property then it has the sampling property, and if an orthogonal scaling function with compact support has the oversampling property then it must be the Haar function χ0,1(t) which is 1 when 0⩽t⩽1 and 0 otherwise. These results imply that, weakening the sampling property to the oversampling proper6g on wavelets is not useful for finding more wavelet families with good decay properties
Keywords :
information theory; signal sampling; wavelet transforms; Haar function; decay properties; orthogonal scaling functions; orthogonal wavelets; oversampling property; sampling rate; scaling functions; space; subspace; wavelet families; Multiresolution analysis; Sampling methods; Signal resolution;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Information Theory, 1994. Proceedings., 1994 IEEE International Symposium on
Conference_Location :
Trondheim
Print_ISBN :
0-7803-2015-8
Type :
conf
DOI :
10.1109/ISIT.1994.394819
Filename :
394819
Link To Document :
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