Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

A Fast Method of Transforming Relaxation Functions Into the Frequency Domain

Published

Author(s)

F I. Mopsik

Abstract

The limits to the error due to truncation of the numeric integration of the onesided Laplace transform of a relaxation function in the time domain into its equivalent frequency domain are established. Separate results are given for large and small . These results show that, for a given , only a restricted range of time samples is needed to perform the computation to a given accuracy. These results are then combined with a known error estimate for integration by cubic splines to give a good estimate for the number of points needed to perform the computation to a given accuracy. For a given data window between t1 and t2, the computation time is shown to be proportional to ln(t1/t2).
Citation
Journal of Research (NIST JRES) -
Volume
104 No. 2

Keywords

cubic spline, error estimate, Laplace transform, numeric integration, numeric transform, relaxation function, time domain

Citation

Mopsik, F. (1999), A Fast Method of Transforming Relaxation Functions Into the Frequency Domain, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed February 29, 2024)
Created January 1, 1999, Updated February 17, 2017