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      • Department of Electrical and Electronics Engineering
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      Fast computation of the ambiguity function and the Wigner distribution on arbitrary line segments

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      Author(s)
      Özdemir, A. K.
      Arıkan, Orhan
      Date
      2001
      Source Title
      IEEE Transactions on Signal Processing
      Print ISSN
      1053-587X
      Publisher
      IEEE
      Volume
      49
      Issue
      2
      Pages
      381 - 393
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      By using the fractional Fourier transformation of the time-domain signals, closed-form expressions for the projections of their auto or cross ambiguity functions are derived. Based on a similar formulation for the projections of the auto and cross Wigner distributions and the well known two-dimensional (2-D) Fourier transformation relationship between the ambiguity and Wigner domains, closed-form expressions are obtained for the slices of both the Wigner distribution and the ambiguity function. By using discretization of the obtained analytical expressions, efficient algorithms are proposed to compute uniformly spaced samples of the Wigner distribution and the ambiguity function located on arbitrary line segments. With repeated use of the proposed algorithms, samples in the Wigner or ambiguity domains can be computed on non-Cartesian sampling grids, such as polar grids.
      Keywords
      Algorithms
      Computer simulation
      Fast Fourier transforms
      Frequency domain analysis
      Probability distributions
      Time domain analysis
      Fractional Fourier transforms
      Wigner distributions (WD)
      Digital signal processing
      Permalink
      http://hdl.handle.net/11693/24898
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/78.902121
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      • Department of Electrical and Electronics Engineering 4011
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