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.
Data Smoothing and Interpolation Using Eighth-Order Algebraic SplinesIEEE Transactions on Signal Processing
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Citation InformationSimon, 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