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B-Spline Signal Processing: Part I-Theory (1993)
| Venue: | IEEE Trans. Signal Processing |
| Citations: | 160 - 31 self |
BibTeX
@ARTICLE{Unser93b-splinesignal,
author = {Michael Unser and Akram Aldroubi and Murray Eden and Life Fellow},
title = {B-Spline Signal Processing: Part I-Theory},
journal = {IEEE Trans. Signal Processing},
year = {1993},
volume = {41},
pages = {821--833}
}
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Abstract
This paper describes a set of efficient filtering techniques for the processing and representation of signals in terms of continuous B-spline basis functions. We first consider the problem of determining the spline coefficients for an exact signal interpolation (direct B-spline transform). The reverse operation is the signal reconstruction from its spline coefficients with an optional zooming factor rn (indirect B-spline transform) . We derive general expressions for the z transforms and the equivalent continuous impulse responses of B-spline interpolators of order n. We present simple techniques for signal differentiation and filtering in the transformed domain. We then derive recursive filters that efficiently solve the problems of smoothing spline and least squares approximations. The smoothing spline technique approximates a signal with a complete set of coefficients subject to certain regularization or smoothness constraints. The least squares approach, on the other hand, uses a reduced number of B-spline coefficients with equally spaced nodes; this technique is in many ways analogous to the application of antialiasing low-pass filter prior to decimation in order to represent a signal correctly with a reduced number of samples.
Keyphrases
b-spline signal processing part i-theory spline coefficient reduced number signal differentiation optional zooming factor rn signal reconstruction certain regularization spaced node low-pass filter transformed domain exact signal interpolation direct b-spline transform reverse operation continuous b-spline basis function b-spline coefficient many way spline technique present simple technique derive general expression equivalent continuous impulse response indirect b-spline transform recursive filter smoothness constraint b-spline interpolators square approximation complete set
