Cardinal Spline Filters: Stability and Convergence to the Ideal Sinc Interpolator
A. Aldroubi, M. Unser, M. Eden
Signal Processing, vol. 28, no. 2, pp. 127–138, August 1992.
The authors provide an interpretation of polynomial spline interpolation as a continuous filtering process. They prove that the frequency responses of the cardinal spline filters converge to the ideal lowpass filter in all Lp-norms with 1 ≤ p < +∞ as the order of the spline tends to infinity. They provide estimates for the resolution errors and the interpolation errors of the various filters. They also derive an upper bound for the error associated with the reconstruction of bandlimited signals using polynomial splines.
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AUTHOR="Aldroubi, A. and Unser, M. and Eden, M.",
TITLE="Cardinal Spline Filters: {S}tability and Convergence to the
Ideal Sinc Interpolator",
JOURNAL="Signal Processing",
YEAR="1992",
volume="28",
number="2",
pages="127--138",
month="August",
note="")
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