2014
DOI: 10.1137/130932533
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Discrete Periodic Extension Using an Approximate Step Function

Abstract: The discrete periodic extension is a technique for augmenting a given set of uniformly spaced samples of a smooth function with auxiliary values in an extension region. If a suitable extension is constructed, the interpolating trigonometric polynomial found via an FFT will accurately approximate the original function in its original interval of definition. The discrete periodic extension is a key construction in the algorithm FC-Gram (Fourier continuation based on Gram polynomials) algorithm. The FC-Gram algor… Show more

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Cited by 5 publications
(1 citation statement)
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“…Having set the theoretical groundwork for a Fourier-informed approach to B-spline fitting, it is essential to note that the B-spline data models presented here need not be restricted to periodic signals. If the data are already represented on an equidistant grid but are not, then strategies for periodic continuation [2,20] should be considered. If the data are scattered, a naive approach would be to interpolate on an equidistant grid, which may add computational overhead to the FFT; however, the non-uniform FFT (NUFFT) [11] is recommended to preserve the efficiency of the FFT.…”
Section: Input Signalmentioning
confidence: 99%
“…Having set the theoretical groundwork for a Fourier-informed approach to B-spline fitting, it is essential to note that the B-spline data models presented here need not be restricted to periodic signals. If the data are already represented on an equidistant grid but are not, then strategies for periodic continuation [2,20] should be considered. If the data are scattered, a naive approach would be to interpolate on an equidistant grid, which may add computational overhead to the FFT; however, the non-uniform FFT (NUFFT) [11] is recommended to preserve the efficiency of the FFT.…”
Section: Input Signalmentioning
confidence: 99%