Abstract
A pair of quadrature mirror filters provides a decomposition of any Hilbert space H as direct sum of orthogonal subspaces by giving a recipe to construct orthonormal bases of the space itself. The resulting subspaces are related to a finite partition of [0, 1) by dyadic intervals. It is known that, under some assumptions on the filter coefficients, the partition can consist of an infinite number of dyadic intervals covering [0, 1) except for a denumerable set. A major application of this fact is the construction of libraries of wavelet packets orthonormal bases of L 2(R) obtained by Meyer, Coifman and Wickerhauser.
We prove that the same result holds if the exceptional set corresponding to the infinite partition has Hausdorff dimension strictly less then 1/2, thus extending the range of the possible wavelet packets orthonormal bases.
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© 1995 Springer Science+Business Media Dordrecht
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Saliani, S. (1995). On the Possible Wavelet Packets Orthonormal Bases. In: Singh, S.P. (eds) Approximation Theory, Wavelets and Applications. NATO Science Series, vol 454. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8577-4_28
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DOI: https://doi.org/10.1007/978-94-015-8577-4_28
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4516-4
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