Fractional Fourier Transform: Duality, Correlation Theorem and Applications

We first start by introducing the fractional Fourier trans-form. We exhibit that the direct relationship between the fractional Fourier transform and Fourier transform can be developed for obtaining the fractional Fourier transform of a function. We then establish the duality property related to the fractional Fourier transform. It is shown that the correlation theorem can be found using the natural link between the convolution and cor-relation definitions in the fractional Fourier domains. For applications, various consequences of the convolution and correlation theorems including the fractional Fourier transform are also in-vestigated in detail.