A cardinal spline approach to wavelets

Authors:
Charles K. Chui and Jian-zhong Wang

Journal:
Proc. Amer. Math. Soc. **113** (1991), 785-793

MSC:
Primary 41A15; Secondary 42C05

DOI:
https://doi.org/10.1090/S0002-9939-1991-1077784-X

MathSciNet review:
1077784

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Abstract: While it is well known that the th order -spline with integer knots generates a multiresolution analysis, , with the th order of approximation, we prove that , where denotes the th order fundamental cardinal interpolatory spline, generates the orthogonal complementary wavelet spaces . Note that for , when the -spline is the characteristic function of the unit interval , our basic wavelet is simply the well-known Haar wavelet. In proving that , we give the exact formulation of , in terms of integer translates of and . This allows us to derive a wavelet decomposition algorithm without relying on orthogonality nor construction of a dual basis.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1077784-X

Keywords:
Wavelets,
cardinal splines,
Euler-Frobenius polynomials,
wavelet decompositions,
algorithms

Article copyright:
© Copyright 1991
American Mathematical Society