Cardinal exponential splines: Part I - Theory and filtering algorithms
Journal
IEEE Transactions on Signal Processing
Journal Volume
53
Journal Issue
4
Date Issued
2005-04-01
Author(s)
Unser, Michael
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 also characterize their stability (Riesz bounds). 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. We derive efficient filtering algorithms for multiresolution signal extrapolation and approximation, extending earlier results for polynomial splines. Finally, we present a new asymptotic error formula that predicts the magnitude and the Nth-order decay of the L2-approximation error as a function of the knot spacing T. © 2005 IEEE.
Subjects
Continuous-time signal processing | Convolution | Differential operators | Green functions | Interpolation | Modulation | Multiresolution approximation | Splines
SDGs
Type
journal article