A Class of Scaled Bessel Sampling Theorems

Sampling theorems for a class of scaled Bessel unitary transforms are presented. The derivations are based on the properties of the generalized Laguerre functions. This class of scaled Bessel unitary transforms includes the classical sine and cosine transforms, but also novel chirp sine and modified Hankel transforms. The results for the sine and cosine transform can also be utilized to yield a sampling theorem, different from Shannon's, for the Fourier transform.