Abstract
For a given λ, the cubic spline smoother is a time-varying linear filter, but it can be approximated by a time-invariant linear filter. It will then be amenable to frequency domain analysis and implementation using the FFT. The FFT algorithm will be compared to the Cholesky algorithm in terms of execution time, accuracy, and memory use. For digital signal processing background, see [1]. Other results on splines in the frequency domain can be found in [2].
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References
Manolakis DG, Ingle VK (2011) Applied digital signal processing. Cambridge University Press, New York
Unser M, Blu T (2007) Self-similarity: part 1-splines and operators. IEEE Trans Signal Process 55:1352–1363
De Nicolao G, Ferrari-Trecate G, Sparacino G (2000) Fast spline smoothing via spectral factorization concepts. Automatica 36:1733–1739
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Weinert, H.L. (2013). FFT Algorithm. In: Fast Compact Algorithms and Software for Spline Smoothing. SpringerBriefs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5496-0_4
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DOI: https://doi.org/10.1007/978-1-4614-5496-0_4
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