УДК 621.396

Об использовании простого способа оценки ошибки интерполяции экспериментальных данных

 

А. В. Кокошкин, В. А. Коротков, К. В. Коротков, Е. П. Новичихин

Институт радиотехники и электроники им. В.А. Котельникова РАН, Фрязинский филиал

 

Статья поступила в редакцию 18 августа 2016 г.

 

Аннотация. В данной работе описано применение простого метода оценки ошибки интерполяции. Этот метод формально не требует исследовать свойства интерполированного сигнала и не имеет явных ограничений при использовании любого метода интерполяции. Естественным ограничением предлагаемого метода является требование такого шага измерений, который обеспечивает адекватное описания свойств исследуемого сигнала.

Ключевые слова: интерполяция, оценка ошибок.

Abstract. Experimental data processing often requires to calculate the value of the signal is measured points – to interpolate measured data. This is useful, for example, to analyze the experimental data, the graphical representation of the results obtained, calculating signal characteristics. Interpolation is almost always accompanied by errors, the knowledge of which can be used to select the interpolation method, the subsequent measurement planning, determining the coordinates measured at the same points.

Typically, a priori information for constructing functional data model is insufficient. Or to build a functional model is fundamentally impossible. Therefore, using standard techniques of interpolation error estimation is very difficult. The task of interpolation of an arbitrary function is not the purpose of our work. The aim of this work is to demonstrate the capabilities of a simple method for estimating the error of interpolation of the experimental data to select the interpolation method, the coordinates of the measuring points, the analysis of the measured data.

The proposed method is based on the following idea. Let the measured values at the points well enough describe the properties of the signal. In order to evaluate the interpolation error, we will evaluate the difference in values between the two interpolations consistently held, with the second interpolation uses as a nodal point values from the first interpolation.

This work describes the use of a simple method of interpolation error estimate. This method does not require formal study the properties of the interpolated signal and has no obvious limitations when using any interpolation method. The natural limitation of this method is the requirement of such a measurement step that provides an adequate description of the properties of the test signal.

Key words: interpolation, error estimation.