Cardinal Exponential Splines
Prof. Michael Unser, EPFL LIB

Meeting • 08 December 2003 • EPFL, BM.4.235

Abstract
Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and self-contained signal processing formulation of exponential splines defined on a uniform grid. We specify the corresponding B-spline basis functions and investigate their reproduction properties (Green function and exponential polynomials). We show that the exponential B-spline framework allows an exact implementation of continuous-time signal processing operators including convolution, differential operators, and modulation, by simple processing in the discrete B-spline domain.