Sampling Theorems for Fractional Laplace Transform of Functions of Compact Support

Linear canonical transform is an integral transform with four parameters and has been proved to be powerful tool for optics, radar system analysis, filter design etc. Fractional Fourier transform and Fresnel transform can be seen as a special case of linear canonical transform with real parameters. Further generalization of linear canonical transform with complex parameters is also developed and Fractional Laplace transform is one of the special case of linear canonical transform with complex entities. Here we have studied the fractional Laplace transform of a periodic function of compact support. New sampling formulae for reconstruction of the functions that are of compact support in fractional Laplace transform domain have been proposed. More specifically it is shown that only (2k+1) coefficients are sufficient to construct any fractional Laplace transform domain of periodic function with compact support, where k is the order of positive highest nonzero harmonic component in the domain.