Generalization of Linear Shift Invariant System in the Fractional Domain

Fractional Fourier transform is one of a flourishing field of active research due to its wide range of applications. It is well-known that fractional Fourier transform is linear, but not shift invariant as that of conventional Fourier transform. Linear shift invariant systems can be expressed in terms of convolution of two functions. Convolution for fractional Fourier transform, defined by Almeida is redefined by Zayed A H in order to satisfy the convolution theorem. Akay O had formulated linear fractional shift invariant system through fractional operators. Purpose of this paper is to define linear fractional shift invariant system in terms of its response to a unit impulse and also to show that fractional type convolution as defined by Zayed, can be used in dealing these linear fractional shift invariant systems as in case of conventional Fourier transform. Mathematics Subject Classification: 44A35