Uncertainty principles related to quaternionic windowed Fourier transform

被引：9
作者：
Bahri, Mawardi [1 ]
Ashino, Ryuichi [2 ]
机构：
[1] Hasanuddin Univ, Dept Math, Makassar 90245, Indonesia
[2] Osaka Kyoiku Univ, Math & Informat, Osaka 5828582, Japan
来源：
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING | 2020年 / 18卷 / 03期
关键词：
Quaternionic Fourier transform; logarithmic uncertainty principle; quaternionic windowed Fourier transform; CONVOLUTION; THEOREMS;
D O I：
10.1142/S0219691320500150
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
In this paper, we first introduce uncertainty principles for the quaternion Fourier transform (QFT). We then provide a different proof of the well-known properties of the quaternionic windowed Fourier transform (QWFT) using properties of the QFT which is a little bit simpler than usual. Based on uncertainty principles for the QFT and the relationship between the QFT and QWFT, we establish uncertainty principles related to the QWFT.
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页数：19
相关论文
共 34 条
[1]   Windowed Fourier transform as an essential digital interferometry tool to study coupled heat and mass transfer [J].
Ahadi, Amirhossein ;
Khoshnevis, Ahmad ;
Saghir, M. Ziad .
OPTICS AND LASER TECHNOLOGY, 2014, 57 :304-317
[2]   Quaternionic curvelet transform [J].
Akila, L. ;
Roopkumar, R. .
OPTIK, 2017, 131 :255-266
[3]   Multidimensional Quaternionic Gabor Transforms [J].
Akila, Lakshmanan ;
Roopkumar, Rajakumar .
ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2016, 26 (03) :985-1011
[4]   The quaternionic affine group and related continuous wavelet transforms on complex and quaternionic Hilbert spaces [J].
Ali, S. Twareque ;
Thirulogasanthar, K. .
JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (06)
[5]  
[Anonymous], 1999, HYPERCOMPLEX SPECTRA
[6]   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
[7]   Convolution Theorems for Quaternion Fourier Transform: Properties and Applications [J].
Bahri, Mawardi ;
Ashino, Ryuichi ;
Vaillancourt, Remi .
ABSTRACT AND APPLIED ANALYSIS, 2013,
[8]   Two-dimensional quaternion wavelet transform [J].
Bahri, Mawardi ;
Ashino, Ryuichi ;
Vaillancourt, Remi .
APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (01) :10-21
[9]   Windowed Fourier transform of two-dimensional quaternionic signals [J].
Bahri, Mawardi ;
Hitzer, Eckhard S. M. ;
Ashino, Ryuichi ;
Vaillancourt, Remi .
APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (08) :2366-2379
[10]   Uncertainty principle for the two sided quaternion windowed Fourier transform [J].
Brahim, Kamel ;
Tefjeni, Emna .
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2020, 11 (01) :159-185
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