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. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 0278081X |
| DOI: | 10.1007/s00034-024-02869-x |
