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Translation Invariance of Orthogonal Multiresolution Analyses of L2(R)

โœ Scribed by A. Bastys

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
138 KB
Volume
9
Category
Article
ISSN
1063-5203

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โœฆ Synopsis

Two numerical characteristics for estimation of translation invariance of a multiresolution analysis (MRA) of L 2 (R) are proposed. These two characteristics are defined either through the scaling function or through the scaling symbol of the MRA. Some simple conditions under which both translation invariance characteristics have similar numerical values were found. Translation invariance of Daubechies' compactly supported scaling function, defined by 2N-length lowpass filter, is of order O(N -1/2 ). We have designed some compactly supported scaling functions having a translation invariance O(N -1 ) and proved that this order of decay is optimal. For any MRA of L 2 (R) a Heisenberg translation uncertainty principle is proved.

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