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      Chirp filtering in the fractional Fourier domain

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      Author
      Dorsch, R. G.
      Lohmann, A. W.
      Bitran, Y.
      Mendlovic, D.
      Ozaktas, H. M.
      Date
      1994-11-10
      Source Title
      Applied Optics
      Print ISSN
      1559-128X
      Electronic ISSN
      2155-3165
      Publisher
      Optical Society of America
      Volume
      33
      Issue
      32
      Pages
      7599 - 7602
      Language
      English
      Type
      Article
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      Abstract
      In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of the Wigner-distribution function by an angle connected with the FRT order. Thus with the FRT tool a chirp and a delta function can be transformed one into the other. Taking the chirp as additive noise, the FRT is used for filtering the line delta function in the appropriate fractional Fourier domain. Experimental filtering results for a Gaussian input function, which is modulated by an additive chirp noise, are shown. Excellent agreement between experiments and computer simulations is achieved.
      Keywords
      Filtering
      Fourier optics
      Fractional fourier transform
      Computer simulation
      Fourier transforms
      Signal filtering and prediction
      Chirp filtering
      Delta function
      Fractional fourier transforms
      Wigner distribution function
      Fourier optics
      Permalink
      http://hdl.handle.net/11693/13633
      Published Version (Please cite this version)
      http://dx.doi.org/10.1364/AO.33.007599
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      • Department of Electrical and Electronics Engineering 3339

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