Data Smoothing and Interpolation Using Eighth-Order Algebraic Splines

Daniel J. Simon

doi:10.1109/tsp.2004.823489

Data Smoothing and Interpolation Using Eighth-Order Algebraic Splines

Daniel J. Simon

Research output: Contribution to journal › Article › peer-review

Abstract

A new type of algebraic spline is used to derive a filter for smoothing or interpolating discrete data points. The spline is dependent on control parameters that specify the relative importance of data fitting and the derivatives of the spline. A general spline of arbitrary order is first formulated using matrix equations. We then focus on eighth-order splines because of the continuity of their first three derivatives (desirable for motor and robotics applications). The spline's matrix equations are rewritten to give a recursive filter that can be implemented in real time for lengthy data sequences. The filter is lowpass with a bandwidth that is dependent on the spline's control parameters. Numerical results, including a simple image processing application, show the tradeoffs that can be achieved using the algebraic splines.

Original language	American English
Journal	IEEE Transactions on Signal Processing
Volume	52
DOIs	https://doi.org/10.1109/tsp.2004.823489
State	Published - Apr 1 2004

Keywords

Algebraic splines
Data smoothing
Image processing
Interpolation
Optimization
Recursive filters
Splines

Disciplines

Aerospace Engineering
Electrical and Computer Engineering
Systems Engineering and Multidisciplinary Design Optimization

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Data Smoothing and Interpolation Using Eighth-Order Algebraic SplFinal published version, 6.65 MBLicense: CC BY

Cite this

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title = "Data Smoothing and Interpolation Using Eighth-Order Algebraic Splines",

abstract = " A new type of algebraic spline is used to derive a filter for smoothing or interpolating discrete data points. The spline is dependent on control parameters that specify the relative importance of data fitting and the derivatives of the spline. A general spline of arbitrary order is first formulated using matrix equations. We then focus on eighth-order splines because of the continuity of their first three derivatives (desirable for motor and robotics applications). The spline's matrix equations are rewritten to give a recursive filter that can be implemented in real time for lengthy data sequences. The filter is lowpass with a bandwidth that is dependent on the spline's control parameters. Numerical results, including a simple image processing application, show the tradeoffs that can be achieved using the algebraic splines.",

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note = "Simon, D.; , {"}Data smoothing and interpolation using eighth-order algebraic splines,{"} Signal Processing, IEEE Transactions on , vol.52, no.4, pp. 1136- 1144, April 2004 doi: 10.1109/TSP.2004.823489",

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N1 - Simon, D.; , "Data smoothing and interpolation using eighth-order algebraic splines," Signal Processing, IEEE Transactions on , vol.52, no.4, pp. 1136- 1144, April 2004 doi: 10.1109/TSP.2004.823489

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N2 - A new type of algebraic spline is used to derive a filter for smoothing or interpolating discrete data points. The spline is dependent on control parameters that specify the relative importance of data fitting and the derivatives of the spline. A general spline of arbitrary order is first formulated using matrix equations. We then focus on eighth-order splines because of the continuity of their first three derivatives (desirable for motor and robotics applications). The spline's matrix equations are rewritten to give a recursive filter that can be implemented in real time for lengthy data sequences. The filter is lowpass with a bandwidth that is dependent on the spline's control parameters. Numerical results, including a simple image processing application, show the tradeoffs that can be achieved using the algebraic splines.

AB - A new type of algebraic spline is used to derive a filter for smoothing or interpolating discrete data points. The spline is dependent on control parameters that specify the relative importance of data fitting and the derivatives of the spline. A general spline of arbitrary order is first formulated using matrix equations. We then focus on eighth-order splines because of the continuity of their first three derivatives (desirable for motor and robotics applications). The spline's matrix equations are rewritten to give a recursive filter that can be implemented in real time for lengthy data sequences. The filter is lowpass with a bandwidth that is dependent on the spline's control parameters. Numerical results, including a simple image processing application, show the tradeoffs that can be achieved using the algebraic splines.

KW - Algebraic splines

KW - Data smoothing

KW - Image processing

KW - Interpolation

KW - Optimization

KW - Recursive filters

KW - Splines

UR - https://engagedscholarship.csuohio.edu/enece_facpub/19

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VL - 52

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

ER -

Data Smoothing and Interpolation Using Eighth-Order Algebraic Splines

Abstract

Keywords

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