Quaternionic one-dimensional fractional Fourier transform

被引：25
作者：
Roopkumar, Rajakumar [1 ]
机构：
[1] Cent Univ Tamil Nadu, Dept Math, Thiruvarur 610101, India
来源：
OPTIK | 2016年 / 127卷 / 24期
关键词：
Fractional Fourier transform; Convolution; Quaternion valued functions; CONVOLUTION; PRODUCT; THEOREM;
D O I：
10.1016/j.ijleo.2016.09.069
中图分类号：
O43 [光学];
学科分类号：
070207 ; 0803 ;
摘要：
In this paper, we introduce quaternionic fractional Fourier transform of integrable (and square integrable) functions on R and prove that it is satisfying all the expected properties like linearity, inversion formula, Parseval's formula, convolution theorem and product theorem. (C) 2016 Elsevier GmbH. All rights reserved.
引用
收藏
页码：11657 / 11661
页数：5
相关论文
共 30 条
[1]   Quaternionic Stockwell transform [J].
Akila, L. ;
Roopkumar, R. .
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2016, 27 (06) :484-504
[2]   Multidimensional Quaternionic Gabor Transforms [J].
Akila, Lakshmanan ;
Roopkumar, Rajakumar .
ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2016, 26 (03) :985-1011
[3]   Ridgelet transform for quarternion-valued functions [J].
Akila, Lakshmanan ;
Roopkumar, Rajakumar .
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2016, 14 (01)
[4]   A natural convolution of quaternion valued functions and its applications [J].
Akila, Lakshmanan ;
Roopkumar, Rajakumar .
APPLIED MATHEMATICS AND COMPUTATION, 2014, 242 :633-642
[5]   Product and convolution theorems for the fractional Fourier transform [J].
Almeida, LB .
IEEE SIGNAL PROCESSING LETTERS, 1997, 4 (01) :15-17
[6]   THE FRACTIONAL FOURIER-TRANSFORM AND TIME-FREQUENCY REPRESENTATIONS [J].
ALMEIDA, LB .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1994, 42 (11) :3084-3091
[7]  
[Anonymous], 1986, REAL COMPLEX ANAL
[8]   An uncertainty principle for quaternion Fourier transform [J].
Bahri, Mawardi ;
Hitzer, Eckhard S. M. ;
Hayashi, Akihisa ;
Ashino, Ryuichi .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (09) :2398-2410
[9]   Two-dimensional quaternion wavelet transform [J].
Bahri, Mawardi ;
Ashino, Ryuichi ;
Vaillancourt, Remi .
APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (01) :10-21
[10]  
ELL TA, 1993, PROCEEDINGS OF THE 32ND IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, P1830, DOI 10.1109/CDC.1993.325510
123