Shifted Linear Interpolation Filter

Hannu Olkkonen, Juuso T. Olkkonen

.

DOI: 10.4236/jsip.2010.11005                

Abstract

Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spline. In this work we show that the interpolation error can be remarkably diminished by using the time-shifted B-spline as an interpolation kernel. We verify by experimental tests that the optimal shift is. In VLSI and microprocessor circuits the shifted linear interpolation (SLI) algorithm can be effectively implemented by the z-transform filter. The interpolation error of the SLI filter is comparable to the more elaborate higher order cubic convolution interpolation.

Keywords

Linear Interpolation, Cubic Convolution, B-splines, VLSI

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	G. Plonka, “Periodic Spline Interpolation with Shifted Nodes,” Journal of Approximation Theory, Vol. 76, No. 1, 1994, pp. 1-20.
[2]	G. Plonka, “Optimal Shift Parameters for Periodic Spline Interpolation,” Numerical Algorithms, Vol. 6, No. 2, 1994, pp. 297-316.
[3]	I. J. Schoenberg, “Contribution to the Problem of Approximation of Equidistant Data by Analytic Functions,” Quarterly of Applied Mathematics, Vol. 4, No. 1, 1946, pp. 45-99, 112-141.
[4]	T. Blu, P. Thevenaz and M. Unser, “Linear interpolation revitalized”, IEEE Trans. Image Process. Vol. 13, No. 5, pp. 710-719, May 2004.
[5]	R. G. Kay, “Cubic Convolution Interpolation for Digital Image Processing,” IEEE Transactions on Acoustics, Speech, Signal Processing, Vol. 29, No. 6, December 1981, pp. 1153-1160.
[6]	P. Thevenaz, T. Blu and M. Unser, “Interpolation Revisited,” IEEE Transactions on Medical Imaging, Vol. 19, No. 7, July 2000, pp. 739-758.
[7]	J. T. Olkkonen and H. Olkkonen, “Fractional Delay Filter Based on B-Spline Transform,” IEEE Signal Processing Letters, Vol. 14, No. 2, February 2007, pp. 97-100.
[8]	J. T. Olkkonen and H. Olkkonen, “Fractional Time-Shift B-Spline Filter,” IEEE Signal Processing Letters, Vol. 14, No. 10, October 2007, pp. 688-691.
[9]	H. Olkkonen and J. T. Olkkonen, “Half Delay B-Spline Filter for Construction of Shift Invariant Wavelet Transform,” IEEE Transactions on Circuits and Systems II, Vol. 54, No. 7, July 2007, pp. 611-615.
[10]	I. W. Selesnick, “The Design of Approximate Hilbert Transform Pairs of Wavelet Bases,” IEEE Transactions on Signal Processing, Vol. 50, No. 5, May 2002, pp. 1144-1152.