Fourier transforms of fractional order and their optical interpretation

  title={Fourier transforms of fractional order and their optical interpretation},
  author={Haldun Memduh Ozaktas and David Mendlovic},
The original definition of the derivatives of a function makes sense only for integral orders, i.e. we can speak of the first or second derivative and so on. However, it is possible to extend the definition of the derivative to noninteger orders by using an elementary property of Fourier transforms. Bracewell shows how fractional derivatives can be used to characterize the discontinuities of certain functions [ 11. An example from the field of optics is related to the Talbot effect [ 2 1, in… CONTINUE READING


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Self - Fourier objects and other selftransform objects

  • A. Lohmann, D. Mendlovic
  • The Fourier transform and its applications

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