Characterizing the Fourier Transform by Phase and Amplitude Preserving Maps

被引：0

作者：

Kuwata S. ^{[1
]}

机构：

[1] Graduate School of Information Sciences, Hiroshima City University, Asaminami-ku, Hiroshima

来源：

International Journal of Applied and Computational Mathematics | 2017年 / 3卷 / Suppl 1期

关键词：

Amplitude; Fourier transform; Orthogonal polynomial; Phase; Unitary transform;

D O I：

10.1007/s40819-017-0407-4

中图分类号：

学科分类号：

摘要：

It is shown that under the Fourier transform F: L 2 (R) → L 2 (R) of an even or odd function φ: R→ C, the invariance of | φ| leads to the invariance or minus invariance of arg φ, and that the inverse holds in an analogous way. Such a relation between the phase and amplitude does not necessarily hold for other integral transforms. This implies that the Fourier transform can be characterized by the phase and amplitude preserving maps. © 2017, Springer (India) Private Ltd.

引用

页码：1149 / 1162

页数：13

共 50 条

[31] Linear integer unconcerned phase-maps Fourier-transform profilometry by changing the angle of projection
Zhong, JG
LASER INTERFEROMETRY X: TECHNIQUES AND ANALYSIS AND APPLICATIONS, PTS A AND B, 2000, 4101 : 273 - 282
[32] Double image encryption based on phase-amplitude hybrid encoding and iterative phase encoding in fractional Fourier transform domains
Wang, Qu
Guo, Qing
Lei, Liang
OPTIK, 2013, 124 (22): : 5496 - 5502
[33] Joint Fourier transform correlation with phase thresholding in the Fourier domain
Michel, HE
Awwal, AAS
OPTICAL ENGINEERING, 1998, 37 (01) : 33 - 37
[34] Importance of the phase and amplitude in the fractional Fourier domain
Alieva, T
Calvo, ML
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 2003, 20 (03): : 533 - 541
[35] Phase amplitude conformal symmetry in Fourier transforms
Kuwata, S.
XXXTH INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (ICGTMP) (GROUP30), 2015, 597
[36] Spatiotemporal amplitude-and-phase reconstruction by Fourier-transform of interference spectra of high-complex-beams
Alonso, Benjamin
Sola, Inigo J.
Varela, Oscar
Hernandez-Toro, Juan
Mendez, Cruz
San Roman, Julio
Zair, Amelle
Roso, Luis
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 2010, 27 (05) : 933 - 940
[37] An Amplitude Preserving S-Transform for Seismic Data Attenuation Compensation
Wang, Benfeng
IEEE SIGNAL PROCESSING LETTERS, 2016, 23 (09) : 1155 - 1159
[38] 4 bits/symbol Phase and Amplitude Modulation on a Single Discrete Eigenvalue for Transmissions based on Nonlinear Fourier Transform
Gui, Tao
Lo, Shun Ka
Zhou, Xian
Lu, Chao
Lau, Alan Pak Tao
Wai, P. K. A.
2017 OPTICAL FIBER COMMUNICATIONS CONFERENCE AND EXHIBITION (OFC), 2017,
[39] Zero products preserving maps from the Fourier algebra of amenable groups
Farsani, Jafar Soltani
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2014, 21 (03) : 523 - 534
[40] Fourier transform spectroscopies derived from amplitude or phase shaping of broadband laser pulses with applications to adaptive control
Montgomery, Matthew A.
Grumstrup, Erik M.
Damrauer, Niels H.
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 2010, 27 (12) : 2518 - 2533

← 1 2 3 4 5 →