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 add...

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...