Spectrum-Related Theories in the Framework of Quadratic Phase Fourier Transform

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-12-20 DOI:10.1002/mma.10642

Sarga Varghese, Manab Kundu

引用次数: 0

Abstract

In this article, new type of convolution and correlation theorems associated with quadratic phase Fourier transform (QPFT) are studied. Applications of that in multiplicative filter design, which may be useful in optics and signal processing to recover the signals, are also discussed. Besides that, the real Paley–Wiener (PW) and Boas theorem for QPFT are proved, which analyses the characteristics of the signals associated with QPFT in the $L^{2}$ domain.

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本文研究了与二次相位傅里叶变换（QPFT）相关的新型卷积和相关定理。文章还讨论了该定理在乘法滤波器设计中的应用，这可能有助于光学和信号处理中的信号恢复。此外，还证明了 QPFT 的实 Paley-Wiener (PW) 和 Boas 定理，分析了 L 2 $$ {L}^2 $$ 域中与 QPFT 相关的信号特征。

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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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.