Local cubic splines on non-uniform grids and real-time computation of wavelet transform
Averbuch, A., Neittaanmäki, P., Shefi, E., & Zheludev, V. (2017). Local cubic splines on non-uniform grids and real-time computation of wavelet transform. Advances in Computational Mathematics, 43(4), 733-758. https://doi.org/10.1007/s10444-016-9504-x
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Advances in Computational MathematicsDate
2017Copyright
© Springer Science+Business Media New York 2016. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
In this paper, local cubic quasi-interpolating splines on non-uniform grids
are described. The splines are designed by fast computational algorithms that utilize
the relation between splines and cubic interpolation polynomials. These splines provide
an efficient tool for real-time signal processing. As an input, the splines use either
clean or noised arbitrarily-spaced samples. Formulas for the spline’s extrapolation
beyond the sampling interval are established. Sharp estimations of the approximation
errors are presented. The capability to adapt the grid to the structure of an object
and to have minimal requirements to the operating memory are of great advantages
for offline processing of signals and multidimensional data arrays. The designed
splines serve as a source for generating real-time wavelet transforms to apply to signals
in scenarios where the signal’s samples subsequently arrive one after the other
at random times. The wavelet transforms are executed by six-tap weighted moving
averages of the signal’s samples without delay. On arrival of new samples, only a couple
of adjacent transform coefficients are updated in a way that no boundary effects
arise.
...


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