Multiwavelet Packets and Frame Packets of $L^2(mathbb{R}^d)$

Proceedings Mathematical Sciences

Biswaranjan Behera¹ 

[1] Department of Mathematics, Indian Institute of Technology, Kanpur 0 0, India$$

关键词: Wavelet;    wavelet packets;    frame packets;    dilation matrix.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The orthonormal basis generated by a wavelet of $L^2(mathbb{R})$ 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 $L^2(mathbb{R}^d)$ 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 $L^2(mathbb{R}^d)$ from the multiwavelet packets.

【 授权许可】

Unknown