Computation of the Fractional Fourier Transform

We have compared two existing routines for the computation of the fast approximate fractional FouriertransformandoneroutineforthediscretefractionalFouriertransform.Westudiedindetail the dierent steps of the implementation and propose our own implementaion as an alternative that overcomes some of the restrictions. We also test an implementation for the discrete fractional Fourier transform, compare the results of the discrete and the fast approximate transforms and describe our own implementation. It is compared with another algo rithm of Pei which is baed on orthogonal projections. The extra computational eort did not seem to be worthwhile in general. Adaptations of our implementation for obtaining discrete sine or cosine transforms are easy. Matlab versions of our implementations are available on the website