RELATIONSHIPS BETWEEN THE RADON-WIGNER AND FRACTIONAL FOURIER-TRANSFORMS

被引:170
作者
LOHMANN, AW [1 ]
SOFFER, BH [1 ]
机构
[1] HUGHES RES LABS,MALIBU,CA 90265
来源
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION | 1994年 / 11卷 / 06期
关键词
D O I
10.1364/JOSAA.11.001798
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
Two recently described transforms are shown to be related. The Radon-Wigner transform is the squared modulus of the fractional Fourier transform. This new theorem may serve to translate signal and image processing results between different signal representations. Some consequences regarding moments are presented, including a new fractional-Fourier-transform uncertainty relation. Implications for processing are suggested.
引用
收藏
页码:1798 / 1811
页数:14
相关论文
共 13 条
[1]  
ALMEIDA LB, UNPUB IMA J APPL MAT
[2]  
de Bruijn N.G., 1973, NIEUW ARCHIEF VOOR W, V21, P205
[3]   EIGENVECTORS AND FUNCTIONS OF THE DISCRETE FOURIER-TRANSFORM [J].
DICKINSON, BW ;
STEIGLITZ, K .
IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING, 1982, 30 (01) :25-31
[4]  
FLANDRIN P, 1986, P INT C ACOUST SPEEC, V4, P2331
[5]  
KAY S, 1985, P IEEE INT C AC SPEE, V3, P1017
[6]  
LI WP, 1987, IEEE T ACOUST SPEECH, V35, P1210
[7]   IMAGE ROTATION, WIGNER ROTATION, AND THE FRACTIONAL FOURIER-TRANSFORM [J].
LOHMANN, AW .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 1993, 10 (10) :2181-2186
[8]   ON NAMIASS FRACTIONAL FOURIER-TRANSFORMS [J].
MCBRIDE, AC ;
KERR, FH .
IMA JOURNAL OF APPLIED MATHEMATICS, 1987, 39 (02) :159-175
[9]   FRACTIONAL FOURIER-TRANSFORMS AND THEIR OPTICAL IMPLEMENTATION .1. [J].
MENDLOVIC, D ;
OZAKTAS, HM .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 1993, 10 (09) :1875-1881
[10]  
NAMIAS V, 1980, J I MATH APPL, V25, P241