Sampling Expansions with Derivatives for Finite Hankel and Other Transforms
Abdul J. Jerri, Dale W. Kreisler · SIAM Journal on Mathematical Analysis · 1975
A sampling expansion involving the samples of a function represented by a finite Hankel transform and the samples of the derivative of the function is derived. Also, the general procedure for obtaining sampling expansions with derivatives for functions represented by other finite integral transforms is outlined. It is shown that in parallel to the known special case of the finite Fourier transform that the advantage of sampling with N derivatives is to increase by $(N + 1)$-fold the asymptotic spacing between the sampling points. The importance of such an advantage for the Hankel transform can be realized in a time-varying or spatial-varying system. Finally, an extension to two dimensions of the sampling theorem with N derivatives for a function having a finite double Fourier transform is stated.