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Engineering LibreTexts

9.3: The Winograd Fourier Transform Algorithm

  • Page ID
    2016
  • The Winograd Fourier transform algorithm (WFTA) uses a very powerful property of the Type-1 index map and the DFT to give a further reduction of the number of multiplications in the PFA. Using an operator notation where \(F_1\) represents taking row DFT's and \(F_2\) represents column DFT's, the two-factor PFA of the equation is represented by

    \[X=F_2F_1x\]

    It has been shown that if each operator represents identical operations on each row or column, they commute. Since \(F_1\) and \(F_2\) represent length \(N_1\) and \(N_2\) DFT's, they commute and the equation can also be written

    N1N1" role="presentation" style="position:relative;" tabindex="0">