Discrete smoothing splines and digital filtration. Theory and applications. (English) Zbl 0704.65005

Hřebíček, Jiří; Šik, František; Veselý, Vítězslav

Apl. Mat. 35, No. 1, 28-50 (1990).

The paper deals with theoretical and applied aspects of discrete smoothing splines and digital filtration. Its aim is to prove the close interconnection between two smoothing approaches, to develop the transfer function which characterizes the smoothing spline as a filter in terms of \(\alpha\) and \(\lambda_ K\) (the eigenvalues of the discrete analogue of \({\mathcal L})\), and to develop the reduction ratio between the original and smoothed data in the same terms. \((\alpha >0\) is the smoothing parameter and \({\mathcal L}:\) \(W^{2,\nu}\to L_ 2\) is a linear bounded operator). Five physical examples are discussed (sinusoidal wave, saw-like waves, rectangular pulse train, etc.)

Reviewer: M.Gaşpar (Iaşi)

MSC:

65D10	Numerical smoothing, curve fitting
65K10	Numerical optimization and variational techniques
41A15	Spline approximation
65D07	Numerical computation using splines
93E11	Filtering in stochastic control theory
93E14	Data smoothing in stochastic control theory

Keywords:

smoothing parameter; digital convolution filter; discrete smoothing splines; digital filtration; transfer function; sinusoidal wave; saw-like waves; rectangular pulse train

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