The wave packet transform associated with the linear canonical transform

被引：14

作者：

Li, Yuan-Min ^{[1
]}

Wei, Deyun ^{[1
]}

机构：

[1] Xidian Univ, Sch Math & Stat, Xian 710071, Peoples R China

来源：

OPTIK | 2015年 / 126卷 / 21期

基金：

中国国家自然科学基金;

关键词：

Wave packet transform; Time-frequency distribution; Linear canonical transform; Wigner distribution; Ambiguity function; TIME-FREQUENCY REPRESENTATIONS; FRACTIONAL FOURIER-TRANSFORM; BAND-LIMITED SIGNALS; PRODUCT THEOREM; CONVOLUTION; DOMAIN; SAMPLES;

D O I：

10.1016/j.ijleo.2015.07.103

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. In this paper, a new kind of wave packet transform (WPT) associated with the LCT is proposed, this new WPT (WPTL) is defined based on the ideal of the LCT and the WPT. Some properties and physical meaning of the WPTL are investigated. In particular, we show a version of the resolution of the identity of WPTL. Moreover, the relationship between the WPTL and the Wigner distribution (WD) is derived. At last, we introduce the concept of the fractional wavepacketgram, which is defined as the modulus square of the WPTL. It is proved that the fractional wavepacketgram is a member of the Cohen class time-frequency distribution where the kernel is a scale dependent ambiguity function. (C) 2015 Elsevier GmbH. All rights reserved.

引用

页码：3168 / 3172

页数：5

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