The Algorithm and Error Analysis of Fractional Fourier Transform

The idea of fractional powers of the Fourier transform operator is a generalization of the Fourier transform. The application of fractional Fourier transform is as widely as Fourier transform's. In this paper, a Matrix algorithm of discrete fractional Fourier transform was proposed, which can be implemented in Matlab platform more effectively. In the numeric simulation test, the image "chess" was encoded with fractional Fourier transform, the encoded image was decoded with fractional Fourier transform. The error analysis test showed the encoded image can be decoded correctly only with the same parameter; this shows its application for information transmission over the Internet.