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Multi-dimensional Dynamical Sampling in Shift-Invariant Spaces Associated with Special Affine Fourier Transform.

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Title: Multi-dimensional Dynamical Sampling in Shift-Invariant Spaces Associated with Special Affine Fourier Transform.
Authors: Ning, Meng1 (AUTHOR) ningmeng1341@stud.tjut.edu.cn, Liu, Bei1 (AUTHOR) liubei1@mail.nankai.edu.cn, Wu, Li-ping1 (AUTHOR) wuliping@email.tjut.edu.cn, Zhang, Qing-yue1 (AUTHOR) jczhangqingyue@163.com
Source: Circuits, Systems & Signal Processing. May2026, Vol. 45 Issue 5, p4088-4117. 30p.
Subjects: Fourier transforms, Sampling theorem, Signal reconstruction, Integral transforms, Mathematical convolutions, Mathematical transformations, Invariant subspaces, Signal processing
Abstract: The multi-dimensional Special Affine Fourier Transformation (SAFT), which generalizes several well-known unitary transformations, has proven to be a valuable tool in signal processing and optics. Previous research has studied the sampling of band-limited signals, but our paper investigates multivariate dynamical sampling in shift-invariant spaces associated with the SAFT. Firstly, we derive various convolution theorems. Then we characterize dynamical sampling in a shift-invariant space through two approaches, the discrete SAFT and the continuous SAFT. In the end, we present two straightforward examples to clarify our main results and demonstrate the superiority of the signal recovery method of the n-dimensional SAFT (nD-SAFT) over the n-dimensional Fourier transform (nD-FT) and the n-dimensional Linear Canonical transform (nD-LCT). [ABSTRACT FROM AUTHOR]
Copyright of Circuits, Systems & Signal Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: The multi-dimensional Special Affine Fourier Transformation (SAFT), which generalizes several well-known unitary transformations, has proven to be a valuable tool in signal processing and optics. Previous research has studied the sampling of band-limited signals, but our paper investigates multivariate dynamical sampling in shift-invariant spaces associated with the SAFT. Firstly, we derive various convolution theorems. Then we characterize dynamical sampling in a shift-invariant space through two approaches, the discrete SAFT and the continuous SAFT. In the end, we present two straightforward examples to clarify our main results and demonstrate the superiority of the signal recovery method of the n-dimensional SAFT (nD-SAFT) over the n-dimensional Fourier transform (nD-FT) and the n-dimensional Linear Canonical transform (nD-LCT). [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Circuits, Systems & Signal Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00034-025-03401-5
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      – Code: eng
        Text: English
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        PageCount: 30
        StartPage: 4088
    Subjects:
      – SubjectFull: Fourier transforms
        Type: general
      – SubjectFull: Sampling theorem
        Type: general
      – SubjectFull: Signal reconstruction
        Type: general
      – SubjectFull: Integral transforms
        Type: general
      – SubjectFull: Mathematical convolutions
        Type: general
      – SubjectFull: Mathematical transformations
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      – SubjectFull: Invariant subspaces
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      – SubjectFull: Signal processing
        Type: general
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      – TitleFull: Multi-dimensional Dynamical Sampling in Shift-Invariant Spaces Associated with Special Affine Fourier Transform.
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            NameFull: Ning, Meng
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            NameFull: Liu, Bei
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            NameFull: Wu, Li-ping
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              M: 05
              Text: May2026
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              Y: 2026
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