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Related Experiment Videos

Fractionalization of the linear cyclic transforms.

T Alieva1, M L Calvo

  • 1Departamento de Optica, Facultad de Fisicas, Universidad Complutense, Madrid, Spain. talieva@eucmos.sim.ucm.es

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 5, 2001
PubMed
Summary

This study establishes a general algorithm for fractionalizing linear cyclic integral transforms, revealing infinite continuous fractional transforms. Two novel fractional Hartley transforms are introduced with proposed optical implementations.

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Area of Science:

  • Optics and Photonics
  • Mathematical Physics
  • Signal Processing

Background:

  • Linear cyclic integral transforms are fundamental in various scientific fields.
  • Fractional calculus extends the concept of differentiation and integration to non-integer orders.
  • The application of fractional transforms in optics offers new possibilities for signal manipulation.

Purpose of the Study:

  • To establish a general algorithm for the fractionalization of linear cyclic integral transforms.
  • To explore the properties of these fractional transforms in the context of optics.
  • To introduce and propose optical implementations for novel fractional transforms.

Main Methods:

  • Development of a general mathematical framework for fractionalizing linear cyclic integral transforms.

Related Experiment Videos

  • Analysis of the theoretical properties of continuous fractional transforms.
  • Design of experimental setups for optical implementation of fractional transforms.

    • Main Results:

    • A general algorithm for fractionalization of linear cyclic integral transforms is established.
    • An infinite number of continuous fractional transforms can be derived from a single cyclic integral transform.
    • Two distinct types of fractional Hartley transforms were introduced and analyzed.

    Conclusions:

    • The fractionalization of linear cyclic integral transforms provides a rich set of related transforms.
    • Fractional transforms possess unique properties relevant to optical applications.
    • The proposed optical implementations pave the way for experimental realization of fractional Hartley transforms.