Stability of a numerical Laplace transform for dielectric measurements

Author

Mopsik, Frederick I.

Author_Institution

Nat. Inst. of Stand. & Technol., Washington, DC, USA

Volume

1

Issue

1

fYear

1994

fDate

2/1/1994 12:00:00 AM

Firstpage

3

Lastpage

8

Abstract

The stability of a numerical Laplace transform used to convert time-domain dielectric loss data into the frequency domain is examined. It is shown that for a transform using cubic spline integration, cubic least squares interpolation over piecewise linearly sampled data and proper endpoint continuations, the uncertainty in the data transformed into the frequency domain is comparable to that of the original data. Specific topics covered include the effect of finite numeric precision of the data, noise spikes and data extrapolation. An analytic expression in terms of modified Bessel functions is developed to estimate the degree of polynomial needed to fit an exponential over a finite range in time. This last development is used to show that a low polynomial degree is needed for a ratio of final to starting time of less than two

Keywords

Bessel functions; Laplace transforms; dielectric loss measurement; interpolation; least squares approximations; splines (mathematics); cubic least squares interpolation; cubic spline integration; data extrapolation; dielectric loss data; dielectric measurements; endpoint continuations; finite numeric precision; modified Bessel functions; noise spikes; numerical Laplace transform; piecewise linearly sampled data; polynomial degree; transform stability; Dielectric losses; Frequency domain analysis; Interpolation; Laplace equations; Least squares methods; Numerical stability; Polynomials; Spline; Time domain analysis; Uncertainty;

fLanguage

English

Journal_Title

Dielectrics and Electrical Insulation, IEEE Transactions on

Publisher

ieee

ISSN

1070-9878

Type

jour

DOI

10.1109/94.300226

Filename

300226