From Signals and Systems to Splines and Vice Versa
Prof. Michael Unser, EPFL LIB

Test Run • 12 September 2003

Abstract
We use an elementary signals and systems formulation to derive and explain the main properties of polynomial splines. We then extend the formulation to cardinal exponential splines. In particular, we show that these splines can be expressed as a linear combination of the integer shifts of the Green function of some underlying differential operator. We construct the corresponding compactly-supported B-spline functions and discuss some interesting connections with basic system theory.