On the Order of Convergence of Natural Cubic Spline Interpolation

1968 ◽  
Vol 5 (1) ◽  
pp. 89-101 ◽  
Author(s):  
Kendall E. Atkinson
Keyword(s):  
Order Of Convergence ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Cubic Spline Interpolation ◽  
Natural Cubic Spline

scholarly journals Notes on EEG Resampling by Natural Cubic Spline Interpolation

2002 ◽  
Vol 6 (4) ◽  
pp. 73-80 ◽  
Author(s):  
Marco Congedo ◽  
Cem Özen ◽  
Leslie Sherlin
Keyword(s):  
Spline Interpolation ◽  
Cubic Spline ◽  
Cubic Spline Interpolation ◽  
Natural Cubic Spline

Computational Straightening of Images of Curved Macromolecular Helices by Cubic Spline Interpolation Facilitates Structural Analysis By Fourier Methods

1985 ◽  
Vol 43 ◽  
pp. 738-739 ◽  
Author(s):  
Alasdair C. Steven ◽  
Robert Stall ◽  
Peter M. Steinert ◽  
Benes L. Trus
Keyword(s):  
Spline Interpolation ◽  
Cubic Spline ◽  
A Posteriori ◽  
Biological Specimen ◽  
Cubic Spline Interpolation ◽  
3 Dimensional ◽  
Density Maps ◽  
Curvilinear Coordinate ◽  
Diffraction Patterns ◽  
Natural Cubic Spline

Powerful methods based on Fourier analysis have been devised for deducing the helical symmetries of macromolecular filaments and reconstructing their 3-dimensional density maps from electron images of negatively stained specimens. However, their applicability is restricted by the requirement that the particles be precisely straight. Only a limited number of specimens are sufficiently rigid to meet this constraint. Filamentous particles that exhibit varying degrees of flexibility constitute a much wider class of specimens, but their curvature impairs the coherence of their diffraction patterns. A solution to this problem is afforded by computational a posteriori straightening, effected by interpolating the digitized images on to a curvilinear coordinate system defined by the curve described by the particle axis. Here, we describe an algorithm for this purpose based on natural cubic spline interpolation, and illustrate its operation with model data and as applied to a flexuous biological specimen.

scholarly journals VLSI Architecture of Cubic SP line Interpolation on FPGA

2019 ◽  
Vol 8 (4) ◽  
pp. 4014-4017
Keyword(s):  
Spline Interpolation ◽  
Vlsi Architecture ◽  
Cubic Spline ◽  
Intrinsic Mode Functions ◽  
Cubic Spline Interpolation ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Data Points ◽  
Previous Proposal ◽  
Natural Cubic Spline

A novel time frequency analysis method was proposed by N.E.Huang known as Hilbert Huang Transform which, can be used for analyzing and processing real world signals. The Intrinsic Mode Functions (IMF) is the key part of this algorithm, in this part the empirically decomposed signal data points uses the cubic spline interpolation for connecting maximum and minimum points to connect lower and upper envelope of the processed signal. This paper presents the real time architecture for hardware implementation of natural cubic spline interpolation. The architecture of proposed cubic spline is using the properties of continuous cubic and linear polynomials. The experimental results showed that our proposed architecture gets better result than previous proposal implemented on Spartan 6 based FPGA board.

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