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Relationship between the ambiguity function coordinate transformations and the fractional Fourier transform

Relation entre la transformation de coordonnÉes de la fonction d’ambiguÏtÉ et la transformation de fourier fractionnaire

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Abstract

It has been shown that the fractional Fourier transform, recently very intensively investigated in mathematics, quantum mechanics, optics and signal processing, can be obtained as a special case of the earlier introduced linear coordinate transformations of the ambiguity function or Wigner distribution. Some applications of the generalized fractional transform on the time-frequency analysis are presented.

Résumé

Il a été montré que la transformation de Fourier fractionnaire, qui a fait l’objet d’études récentes intensives en mathématique, en mécanique quantique, en optique et en traitement du signal, peut-être obtenue comme cas spécial des transformations de coordonnées linéaires de la fonction d’ambiguïté ou de la distribution de Wigner. Quelques applications de la transformation de Fourier fractionnaire à l’analyse temps-fréquence sont présentées.

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Correspondence to Igor DjuroviĆ or LJubiša StankoviĆ.

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DjuroviĆ, I., StankoviĆ, L. Relationship between the ambiguity function coordinate transformations and the fractional Fourier transform. Ann. Télécommun. 53, 316–319 (1998). https://doi.org/10.1007/BF02997688

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Key words

  • Fourier transform
  • Fractional number
  • Mathematical transformation
  • Ambiguity function
  • Frequency time representation
  • Signal analysis

Mots clés

  • Transformation Fourier
  • Nombre fractionnaire
  • Transformation mathématique
  • Fonction ambiguïté
  • Représentation temps fréquence
  • Analyse signal