FRFT

fractional FFT, modified version of Miki Elad's code

Contents

Description

Y = FRFT(X,ALPHA)
    X is a N-by-1 column vector  or an N-by-s matrix
    if X is a vector, perform FRFT on the vector with fraction alpha
    if X is a matrix and alpha is a constant vector with the same column
    size as X, then perform FRFT on each X(:,j)  with fraction
    alpha(j). When alpha is a constant and X is a matrix, perform FRFT
    on each X(:,j) with the same fraction alpha.

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Modefied version of Miki Elad's Fractional Fourier Transform, computing
the transform

    y[n]=sum_{k=-N/2}^{N/2-1} x(k)*exp(-i*2*pi*k*n*alpha)  n=-N/2, ...,N/2-1

So that for alpha=1/N we get the regular FFT, and for alpha=-1/N we get
the regular   IFFT.

Synopsis: y = frFT(x,alpha)

Inputs -   x - an N-entry vector to be transformed or an N-by-s matrix
           alpha - the scaling factor (in the Pseudo-Polar it is in the range [-1/N,+1/N]

Outputs-   y - the transformed result as an N-entries vector

Written by Michael Elad on March 20th, 2005.
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Examples

         x     = randn(5,3);
         alpha = [1/3,1/4,1/5];
         y     = frFT(x,alpha);

See also

ADJFRFT, PPFT, ADJPPFT, INVPPFTCG.

Copyright

Copyright (C) 2011. Xiaosheng Zhuang, University of Osnabrueck

Update History

modified by Morteza Shahram on Jan 30, 2008. make the index k symmetric,
also change the code to the case where N can be an odd number
modified by  Xiaosheng zhuang on Nov. 9, 2010. allowing input x to be an
N-by-s matrix. Do the frft on each column

Published with MATLAB® 7.10