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Application of Fractional Fourier Transform to Hologram Formation of a Moving Acoustic Source.

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Názov: Application of Fractional Fourier Transform to Hologram Formation of a Moving Acoustic Source.
Autori: Pereselkov, Sergey, Kuz'kin, Venedikt, Ehrhardt, Matthias, Tkachenko, Sergey, Pereselkov, Alexey, Ladykin, Nikolay
Zdroj: Fractal & Fractional; Nov2025, Vol. 9 Issue 11, p715, 26p
Predmety: HOLOGRAPHY, FOURIER transforms, ACOUSTIC radiators, SIGNAL processing, ACOUSTIC generators, ACOUSTIC localization, ACOUSTIC waveguides, DIFFRACTION patterns
Abstrakt: This paper examines how the fractional Fourier transform (FrFT) can be used to form and analyze acoustic holograms produced by a moving, linear, frequency-modulated (LFM) source in a shallow water waveguide. In these environments, the source sound field creates an interference pattern, referred to as a two-dimensional interferogram, which represents the distribution of acoustic intensity in the frequency–time domain. This interferogram consists of parallel interference fringes. Consequently, focal points are formed and aligned along a straight line in the source hologram, which is represented by the two-dimensional Fourier transform of the interferogram. We have developed a holographic method for constructing the interferogram of an LFM source signal and transforming it into a Fourier hologram based on FrFT in the presence of strong noise. A key finding of this study is that the FrFT-based holographic method enables localized focal regions to emerge from modal interference even under high-intensity noise conditions. The positions of these focal spots are directly related to the source parameters, enabling the estimation of key characteristics such as the distance and velocity of the LFM source. We analyzed the effectiveness of the FrFT-based holographic method through numerical experiments in the 100–150 Hz frequency band. The results demonstrate the method's high noise immunity for source localization in realistic shallow water environments under strong noise. [ABSTRACT FROM AUTHOR]
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Application of Fractional Fourier Transform to Hologram Formation of a Moving Acoustic Source.
– Name: Author
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  Data: <searchLink fieldCode="AR" term="%22Pereselkov%2C+Sergey%22">Pereselkov, Sergey</searchLink><br /><searchLink fieldCode="AR" term="%22Kuz'kin%2C+Venedikt%22">Kuz'kin, Venedikt</searchLink><br /><searchLink fieldCode="AR" term="%22Ehrhardt%2C+Matthias%22">Ehrhardt, Matthias</searchLink><br /><searchLink fieldCode="AR" term="%22Tkachenko%2C+Sergey%22">Tkachenko, Sergey</searchLink><br /><searchLink fieldCode="AR" term="%22Pereselkov%2C+Alexey%22">Pereselkov, Alexey</searchLink><br /><searchLink fieldCode="AR" term="%22Ladykin%2C+Nikolay%22">Ladykin, Nikolay</searchLink>
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  Data: Fractal & Fractional; Nov2025, Vol. 9 Issue 11, p715, 26p
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22HOLOGRAPHY%22">HOLOGRAPHY</searchLink><br /><searchLink fieldCode="DE" term="%22FOURIER+transforms%22">FOURIER transforms</searchLink><br /><searchLink fieldCode="DE" term="%22ACOUSTIC+radiators%22">ACOUSTIC radiators</searchLink><br /><searchLink fieldCode="DE" term="%22SIGNAL+processing%22">SIGNAL processing</searchLink><br /><searchLink fieldCode="DE" term="%22ACOUSTIC+generators%22">ACOUSTIC generators</searchLink><br /><searchLink fieldCode="DE" term="%22ACOUSTIC+localization%22">ACOUSTIC localization</searchLink><br /><searchLink fieldCode="DE" term="%22ACOUSTIC+waveguides%22">ACOUSTIC waveguides</searchLink><br /><searchLink fieldCode="DE" term="%22DIFFRACTION+patterns%22">DIFFRACTION patterns</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper examines how the fractional Fourier transform (FrFT) can be used to form and analyze acoustic holograms produced by a moving, linear, frequency-modulated (LFM) source in a shallow water waveguide. In these environments, the source sound field creates an interference pattern, referred to as a two-dimensional interferogram, which represents the distribution of acoustic intensity in the frequency–time domain. This interferogram consists of parallel interference fringes. Consequently, focal points are formed and aligned along a straight line in the source hologram, which is represented by the two-dimensional Fourier transform of the interferogram. We have developed a holographic method for constructing the interferogram of an LFM source signal and transforming it into a Fourier hologram based on FrFT in the presence of strong noise. A key finding of this study is that the FrFT-based holographic method enables localized focal regions to emerge from modal interference even under high-intensity noise conditions. The positions of these focal spots are directly related to the source parameters, enabling the estimation of key characteristics such as the distance and velocity of the LFM source. We analyzed the effectiveness of the FrFT-based holographic method through numerical experiments in the 100–150 Hz frequency band. The results demonstrate the method's high noise immunity for source localization in realistic shallow water environments under strong noise. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Fractal & Fractional is the property of MDPI 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: 10.3390/fractalfract9110715
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      – Code: eng
        Text: English
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        PageCount: 26
        StartPage: 715
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        Type: general
      – SubjectFull: FOURIER transforms
        Type: general
      – SubjectFull: ACOUSTIC radiators
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      – SubjectFull: SIGNAL processing
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      – SubjectFull: ACOUSTIC localization
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      – SubjectFull: DIFFRACTION patterns
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    Titles:
      – TitleFull: Application of Fractional Fourier Transform to Hologram Formation of a Moving Acoustic Source.
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            NameFull: Pereselkov, Sergey
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            NameFull: Kuz'kin, Venedikt
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            NameFull: Pereselkov, Alexey
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              M: 11
              Text: Nov2025
              Type: published
              Y: 2025
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