可交换PR正交多滤波器组的充分必要条件

Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136) Pub Date : 1997-11-02 DOI:10.1109/ACSSC.1997.679107

K. Johnson

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引用次数: 0

摘要

构造基于多小波的滤波器组(多滤波器)比构造标量小波滤波器更困难，部分原因是矩阵乘法的非交换性阻止了标量小波“翻转构造”的平凡扩展。交换多滤波器通过允许使用翻转结构来避免这个问题，从而简化了设计过程。本文给出了分析型多滤波器的多相分量的一个条件，该条件是多滤波器除实现完全的重构和正交性外，还能实现交换性的充分必要条件。这种情况涉及的矩阵的形式类似于出现在各种其他上下文中，其中一些讨论。文中给出了满足上述条件的多滤波器的简单例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A necessary and sufficient condition for commutative PR orthogonal multifilter banks

Constructing multiwavelet-based filter banks (multifilters) is more difficult than constructing scalar wavelet filters, partly because the noncommutativity of matrix multiplication prevents a trivial extension of the scalar wavelet "flip construction". Commutative multifilters avoid this problem by allowing the flip construction to be used, thereby simplifying the design process. This paper presents a condition on the polyphase components of the analysis multifilters which is necessary and sufficient for the multifilters to achieve commutativity in addition to perfect reconstruction and orthogonality. This condition involves matrices of a form similar to that appearing in various other contexts, some of which are discussed. The paper includes simple examples of multifilters satisfying the condition obtained.

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Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136)

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