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The shiftability of some wavelet bases

✍ Scribed by Qiao Wang

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
305 KB
Volume
40
Category
Article
ISSN
0898-1221

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✦ Synopsis

An explicit functional called the shiftability value of wavelet basis, which measures a deviation from translation-invariance, is studied. For functions Β’ with Ikbll -1, it lies in (0,1] with the value 1 being best possible. The relation between the shiftability value rv of the father wavelet and the corresponding value rw of the mother wavelet is given. The shiftability value of Meyer's wavelet and the B-spline wavelets is computed. For Meyer's wavelet, we prove that rw = 3rv -2 and demonstrate how to control the shiftability value by properly designing the wavelet. For the B-spline wavelet of order n, we give the asymptotical relation ~(n).w "~ 3r~ n)--2, and show r(v n)---* 1 as n -* ~. The family of B-spline wavelets contains several well-known wavelets such as Franklin's wavelet, Battle's wavelet, and Lemarid's wavelet, which makes our results potentially useful. (~) 2000 Elsevier Science Ltd. All rights reserved.

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We first show that by combining monodimensional filter banks one can obtain nonseparable filter banks. We then give necessary conditions for these filter banks to generate orthonormal and regular wavelets. Finally, we establish that some of these filter banks lead to arbitrarily smooth, nonseparable