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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.
شبیه سازی مقاله در مورد درونیابی و صاف کردن داده با عنوان Data Smoothing and Interpolation Using Eighth-order Algebraic Splines