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Discrete splines and spline filters

Content Provider	IEEE Xplore Digital Library
Author	Ustuner, K.F. Ferrari, L.A.
Copyright Year	1992
Abstract	An equation is derived for the Z transform of discrete polynomial splines for the general case of nonuniform knots. Two filter structures are provided for the computation and analysis of discrete splines, one for the one-sided factorial function representation and one for the B-spline representation. The filter inputs are the coefficient sequence and the corresponding knot set and the outputs are the discrete spline and its differences. The filter structures supply the input-output relations that can be used to analyze the effects of different patterns of knot nonuniformities given the coefficients, or vice versa. Digital filters with discrete spline unit-sample responses are analyzed. It is shown that filtering with a discrete spline filter can be implemented in two stages: the first stage is an MA filter with as many nodes as there are knots. and the second stage is an AR filter which performs successive summations. Because only the first stage involves multiplications, filters with large ratios of (length of unit-sample response) to (number of knots) can be implemented very efficiently.<>
Sponsorship	IEEE Circuits and Systems Society
Starting Page	417
Ending Page	422
Page Count	6
File Size	483499
File Format	PDF
ISSN	10577130
Volume Number	39
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1992-07-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Digital filters Filtering Approximation methods Digital signal processing Equations Discrete transforms Spline Pattern analysis Convergence
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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