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Cited by 69Mathematical Analysis and Transform MethodsSparse and Compressive Sensing TechniquesAdvanced Electrical Measurement Techniques

On fractional Fourier transform moments

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Alieva, T., Bastiaans, M.J.·2000·IEEE Signal Processing Letters
DOI 10.1109/97.873570
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Abstract

Based on the relation between the ambiguity function represented in a quasipolar coordinate system and the fractional power spectra, the fractional Fourier transform (FT) moments are introduced. Important equalities for the global second order fractional FT moments are derived, and their applications for signal analysis are discussed. The connection between the local moments and the angle derivative of the fractional power spectra is established. This permits us to solve the phase retrieval problem if only two close fractional power spectra are known.

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  • For mono-component signals, the required fractional Fourier transformation order can be found based on the fractional moments of the signal.

    “Alternatively, for mono-component signals, the required fractional Fourier transformation order can also be found based on the fractional moments of the signal.”

    From Short-time fourier transform: two fundamental properties and an optimal implementation (2003) · cites this paper as [34]

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Authors
Alieva, T., & Bastiaans, M. J.
Affiliations
Eindhoven University of Technology (NL)
ORCID
Alieva, T.
Venue
IEEE Signal Processing Letters
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2000-11
Volume
7
Issue
11
Pages
320-323
ISSN
  • 1070-9908 (ISSN-L)
  • 1558-2361
DOI
10.1109/97.873570
OpenAlex
W2166808759
Cited by
69
References
0
Citations by year
2024: 1 · 2023: 2 · 2022: 2 · 2021: 1 · 2019: 2 · 2018: 1 · 2017: 3 · 2016: 2 · 2015: 3 · 2014: 3 · 2013: 2 · 2012: 5
FWCI
10.79
Type
journal article
Language
en
Open access
Licence
Locations
  • IEEE Signal Processing Letters (publishedVersion)
  • TU/e Research Portal (submittedVersion)
  • TU/e Research Portal (submittedVersion, other-oa)
Topics
  • Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
  • Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Electrical Measurement Techniques
Keywords
fractional Fourier transform, fractional moments, ambiguity function, second moment, phase retrieval, signal analysis

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