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Uniqueness of Short-Time Linear Canonical Transform Phase Retrieval for Bandlimited Signals.

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Title: Uniqueness of Short-Time Linear Canonical Transform Phase Retrieval for Bandlimited Signals.
Authors: Li, Ying1 (AUTHOR) liying@stud.tjut.edu.cn, Zhang, Qingyue1 (AUTHOR) jczhangqingyue@163.com, Li, Rui1 (AUTHOR) lrsx@163.com, Liu, Bei2 (AUTHOR) liubei1@mail.nankai.edu.cn
Source: Circuits, Systems & Signal Processing. Feb2025, Vol. 44 Issue 2, p1120-1137. 18p.
Subjects: Generalized spaces, Sampling theorem, Standard deviations, Signals & signaling
Abstract: The short-time Fourier transform phase retrieval problem is reconstructing a signal from its short-time Fourier transform magnitude. This phase retrieval approach has a wide range of applications across various fields, such as ptychography and frequency-resolved optical gating. A recent contribution by Wellershof established that the complex-valued signals in the Paley–Wiener space can be uniquely recovered (up to global phase) by their short-time Fourier transform magnitudes sampled at 1 4 Ω Z × { ω 0 , ω 1 } . In this paper, we generalize Wellershof's findings to the case of short-time linear canonical transform phase retrieval. Specifically, we demonstrate that complex-valued signals in the generalized Paley–Wiener space can be uniquely recovered (up to global phase) by their short-time linear canonical transform magnitudes sampled at b 4 Ω Z × ω 0 , ω 1 . Since the generalized Paley–Wiener space includes a broader class of signals, our results expand the application scope of the phase retrieval. Finally, we apply short-time linear canonical transform and short-time Fourier transform to the bandlimited signals and compare their standard deviation and energy concentration rate. [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: <searchLink fieldCode="JN" term="%22Circuits%2C+Systems+%26+Signal+Processing%22">Circuits, Systems & Signal Processing</searchLink>. Feb2025, Vol. 44 Issue 2, p1120-1137. 18p.
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– Name: Abstract
  Label: Abstract
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  Data: The short-time Fourier transform phase retrieval problem is reconstructing a signal from its short-time Fourier transform magnitude. This phase retrieval approach has a wide range of applications across various fields, such as ptychography and frequency-resolved optical gating. A recent contribution by Wellershof established that the complex-valued signals in the Paley–Wiener space can be uniquely recovered (up to global phase) by their short-time Fourier transform magnitudes sampled at 1 4 Ω Z × { ω 0 , ω 1 } . In this paper, we generalize Wellershof's findings to the case of short-time linear canonical transform phase retrieval. Specifically, we demonstrate that complex-valued signals in the generalized Paley–Wiener space can be uniquely recovered (up to global phase) by their short-time linear canonical transform magnitudes sampled at b 4 Ω Z × ω 0 , ω 1 . Since the generalized Paley–Wiener space includes a broader class of signals, our results expand the application scope of the phase retrieval. Finally, we apply short-time linear canonical transform and short-time Fourier transform to the bandlimited signals and compare their standard deviation and energy concentration rate. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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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/s00034-024-02869-x
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Sampling theorem
        Type: general
      – SubjectFull: Standard deviations
        Type: general
      – SubjectFull: Signals & signaling
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      – TitleFull: Uniqueness of Short-Time Linear Canonical Transform Phase Retrieval for Bandlimited Signals.
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            – D: 01
              M: 02
              Text: Feb2025
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              Y: 2025
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            – TitleFull: Circuits, Systems & Signal Processing
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