A Convolution Theorem for the Two Dimensional Fractional Fourier Transform in Generalized Sense

The two dimensional fractional Fourier transform (FrFT), which is a generalization of the Fourier transform, has many applications in several areas including signal processing and optics. Signal processing and pattern recognition algorithms make extensive use of convolution. In pattern recognition, convolution is an important tool because of its translation invariance properties. Also convolution is a powerful way of characterizing the input-output relationship of time invariant linear system. In this paper the convolution theorem for two dimensional fractional Fourier transform in the generalized sense is proved.