# pyewt.pseudopolarfft module

pyewt.pseudopolarfft.PPFFT(X)

  Pseudo Polar Fourier Transform

  Parameters:

    X (-) – Input image

  Returns:

    - Y – Pseudo polar Fourier transform (vertical=theta, horizontal=radius)

  Return type:

    2D nd-array

  Notes

  This function performs the pseudo (recto) polar Fourier transform of the image X. If X is of size N x N, the output will have size 2N x 2N. If X is not square, it is squared before the transform (padded with 0s). Also the size is increased to get even numbers of rows and columns.

  This code is inspired by the Matlab code provided by Michael Elad in his Polarlab toolbox: https://elad.cs.technion.ac.il/software/

  Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (01/23/2025)

pyewt.pseudopolarfft.my_FRFT(x, alpha)

  Fractional Fourier Transform

  Parameters:

    - x (-) – image to transform

    - alpha (-) – for pseudo-polar it should be in the range [-1/N,1/N] where is the number of elements in x

  Returns:

    - y – transformed vector of an N elements input

  Return type:

    1D nd-array

  Notes

  This function computes the fractional Fourier Transform

  y[n]=sum_{k=0}^{N-1} x(k) e^{-i 2pi k n alpha} ; n=0,1,…, N-1

  So that for alpha=1/N we have the regular FFT, anf for alpha=-1/n we have the regular IFFT

  This code is a translation of the Matlab code provided by Michael Elad in his Polarlab toolbox: https://elad.cs.technion.ac.il/software/

  Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (01/23/2025)

pyewt.pseudopolarfft.my_FRFT_Centered(x, alpha)

  Centered Fractional Fourier Transform

  Parameters:

    - x (-) – image to transform

    - alpha (-) – for pseudo-polar it should be in the range [-1/N,1/N] where is the number of elements in x

  Returns:

    - y – transformed vector of an N elements input

  Return type:

    1D nd-array

  Notes

  This function computes the fractional Fourier Transform

  y[n]=sum_{k=0}^{N-1} x(k) e^{-i 2pi k n alpha} ; n=0,1,…, N-1

  So that for alpha=1/N we have the regular FFT, anf for alpha=-1/n we have the regular IFFT

  This code is a translation of the Matlab code provided by Michael Elad in his Polarlab toolbox: https://elad.cs.technion.ac.il/software/

  Author: Jerome Gilles Institution: San Diego State University Version: 1.0 (01/23/2025)