FRACTIONAL FOURIER TRANSFORM: DUALITY, CORRELATION THEOREM AND APPLICATIONS

We first start by introducing the fractional Fourier transform. 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 correlation definitions in the fractional Fourier domains. For applications, various consequences of the convolution and correlation theorems including the fractional Fourier transform are also investigated in detail.