Discrete Bessel Functions for Representing the Class of Finite Duration Decaying Sequences

Bessel functions have shown to be particularly suitable for representing certain classes of signals, since using these basis functions may results in fewer components than using sinusoids. However, as there are no closed form expressions available for such functions, approximations and numerical methods have been adopted for their computation. In this paper the functions called discrete Bessel functions that are expressed as a finite expansion are defined. It is shown that in a finite interval a finite number of such functions that perfectly match Bessel functions of integer order exist. For finite duration sequences it is proven that the subspace spanned by a set of these functions is able to represent the class of finite duration decaying sequences.