Data smoothing by cubic spline filters

Author

Gung Feng

Author_Institution

Inst. de la Commun. Parlee, Stendhal Univ., Grenoble

Volume

46

Issue

10

fYear

1998

fDate

10/1/1998 12:00:00 AM

Firstpage

2790

Lastpage

2796

Abstract

In this correspondence, a digital filter that allows the computation of a smoothing cubic spline for equispaced data with a constant control parameter is proposed. Filters to compute its first and second derivatives are also presented. Derived from the classical matrix solution, these filters offer an efficient way to calculate smoothed data and its derivatives, especially when the length of data is long. Moreover, these filters have been found to possess several interesting properties. For instance, the smoothing filter is a low-pass filter with the maximum flatness property. In addition, a useful relation between the filter bandwidth and the control parameter is established, which can be used for its optimal choice in practice. The proposed filters can easily be implemented either with a recursive structure for off-line processing or with a nonrecursive implementation for real-time processing

Keywords

Toeplitz matrices; digital filters; filtering theory; low-pass filters; recursive filters; smoothing methods; splines (mathematics); classical matrix solution; constant control parameter; cubic spline filters; data smoothing; digital filter; equispaced data; filter bandwidth; low-pass filter; maximum flatness property; nonrecursive implementation; off-line processing; real-time processing; recursive structure; smoothing filter; Bandwidth; Digital filters; Optimal control; Smoothing methods; Spline; Symmetric matrices;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.720380

Filename

720380