四元子空间 Gabor 帧及其对偶

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-14 DOI:10.1007/s00006-024-01342-x

Yun-Zhang Li, Xiao-Li Zhang

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引用次数: 0

摘要

由于其在信号分析和图像处理中的潜在应用，四元傅里叶分析受到越来越多的关注。本文探讨了时频移动参数乘积为有理数条件下的四元子空间 Gabor 帧。我们用四元数 Zak 变换矩阵来描述子空间四元数 Gabor 帧。对于任意子空间 Gabor 框架，我们给出了其 I 型和 II 型 Gabor 对偶的参数表达式，并描述了 I 型和 II 型 Gabor 对偶的唯一性。作为应用，给定整个空间 \(L^{2}({\mathbb {R}}^{2},\,{\mathbb {H}})\)的 Gabor 框架，我们给出其所有 Gabor 对偶的参数表达式，并推导出其唯一的 Gabor 对偶类型 II。我们还提供了一些实例。

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Quaternionic Subspace Gabor Frames and Their Duals

Due to its potential application in signal analysis and image processing, quaternionic Fourier analysis has received increasing attention. This paper addresses quaternionic subspace Gabor frames under the condition that the products of time-frequency shift parameters are rational numbers. We characterize subspace quaternionic Gabor frames in terms of quaternionic Zak transformation matrices. For an arbitrary subspace Gabor frame, we give a parametric expression of its Gabor duals of type I and type II, and characterize the uniqueness Gabor duals of type I and type II. And as an application, given a Gabor frame for the whole space \(L^{2}({\mathbb {R}}^{2},\,{\mathbb {H}})\), we give a parametric expression of its all Gabor duals, and derive its unique Gabor dual of type II. Some examples are also provided.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.