6533b85afe1ef96bd12b9f66

RESEARCH PRODUCT

Quasi-interpolating and Smoothing Local Splines

Pekka NeittaanmäkiValery A. ZheludevAmir Averbuch

subject

Spline (mathematics)Smoothing splineComputer Science::GraphicsWaveletFinite impulse responseComputer scienceApproximation propertyComputationApplied mathematicsArray data typeSmoothingMathematics::Numerical Analysis

description

In this chapter, local quasi-interpolating and smoothing splines are described. Although approximation properties of local spline are similar to properties of the global interpolating and smoothing splines, their design does not require the IIR filtering of the whole data array. The computation of a local spline value at some point utilizes only a few adjacent grid samples. Therefore, local splines can be used for real-time processing of signals and for the design of FIR filter banks generating wavelets and wavelet frames (Chaps. 12 and 14). In the chapter, local splines of different orders are designed and their approximation properties are established which are compared with the properties of global splines. Compactly supported generators of the spline spaces are described.

yearjournalcountryeditionlanguage
2015-08-28
https://doi.org/10.1007/978-3-319-22303-2_5