Windowed special affine Fourier transform

被引：11
|
作者：
Shah, Firdous A. [1 ]
Teali, Aajaz A. [1 ]
Tantary, Azhar Y. [1 ]
机构：
[1] Univ Kashmir, Dept Math, South Campus, Anantnag 192101, Jammu & Kashmir, India
来源：
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2020年 / 11卷 / 03期
关键词：
Window function; Special affine Fourier transform; Discrete transform; Series expansion; Poisson summation formula; Uncertainty principle; LINEAR CANONICAL TRANSFORM; BAND-LIMITED SIGNALS; UNCERTAINTY PRINCIPLE; CORRELATION THEOREMS; PITTS INEQUALITY; CONVOLUTION;
D O I：
10.1007/s11868-019-00319-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
With the aim to circumvent the limitations of the special affine Fourier transform, we introduce a novel time-frequency transform namely the windowed special affine Fourier transform. We initiate our investigation by studying some fundamental properties of the proposed transform such as orthogonality relation, inversion formula and characterization of the range by employing the machinery of special affine Fourier transforms and operator theory. Continuing our endeavour, we propose a discrete analogue of the proposed windowed special affine Fourier transform and obtain the corresponding reconstruction formula. Besides, some potential applications of this new transform including windowed series expansion, Poisson summation formula, Paley-Wiener criterion and uncertainty principles are also given.
引用
收藏
页码：1389 / 1420
页数：32
相关论文
共 50 条
  • [31] Windowed Fourier transform for fringe pattern analysis
    Kemao, Q
    [J]. APPLIED OPTICS, 2004, 43 (13) : 2695 - 2702
  • [32] Shape Analysis with Anisotropic Windowed Fourier Transform
    Melzi, Simone
    Rodola, Emanuele
    Castellani, Umberto
    Bronstein, Michael M.
    [J]. PROCEEDINGS OF 2016 FOURTH INTERNATIONAL CONFERENCE ON 3D VISION (3DV), 2016, : 470 - 478
  • [33] An improved windowed Fourier transform for fringe demodulation
    Quan, C.
    Niu, H.
    Tay, C. J.
    [J]. OPTICS AND LASER TECHNOLOGY, 2010, 42 (01): : 126 - 131
  • [34] On the windowed Fourier transform and wavelet transform of almost periodic functions
    Partington, JR
    Ünalmis, B
    [J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2001, 10 (01) : 45 - 60
  • [35] Special Affine Fourier Transform for Space-Time Algebra Signals
    Hitzer, Eckhard
    [J]. ADVANCES IN COMPUTER GRAPHICS, CGI 2021, 2021, 13002 : 658 - 669
  • [36] Uncertainty Principle for the Short-time Special Affine Fourier Transform
    Rui Li
    Qingyue Zhang
    [J]. Circuits, Systems, and Signal Processing, 2021, 40 : 4594 - 4613
  • [37] Uncertainty Principle for the Short-time Special Affine Fourier Transform
    Li, Rui
    Zhang, Qingyue
    [J]. CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2021, 40 (09) : 4594 - 4613
  • [38] Inversion formula for the windowed Fourier transform, II
    Sun, Xudong
    Sun, Wenchang
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2013, 38 (01) : 21 - 34
  • [39] Analysis of financial indices by means of the windowed Fourier transform
    J. Tenreiro Machado
    Fernando B. Duarte
    Gonçalo Monteiro Duarte
    [J]. Signal, Image and Video Processing, 2012, 6 : 487 - 494
  • [40] Special affine Fourier transform of tempered distributions and pseudo-differential operators
    Kumar, Manish
    [J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2024, 35 (10) : 561 - 576
12345