Multiwavelet packets and frame packets of L²(\mathbb R^d)

2001/08/31 by Biswaranjan Behera
Mathematics · #math.FA #msc:42C40

paper · pdf

published as Proc. Indian Acad. Sci. Math. Sc., vol. 111, no. 4 (2001) pp. 439-463 · Revised, journal reference added

arxiv created 2002/01/10 · arxiv updated 2009/11/30

Abstract

The orthonormal basis generated by a wavelet of L²(\mathbb R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L²(\mathbb R^d) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized to this setting. Further, we show how to construct various orthonormal bases of L²(\mathbb R^d) from the multiwavelet packets.

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