Study of Exponential Laplace Transformation and Its Applications to Analysis of Transient Phenomena

Trans. Electrical Engineering in Japan, Vol. 102C, No. 2, pp.77-84, April 1982


Numerical Fourier-Laplace transform technique is used widely in alalysis of transient phenomena in electric circuits, frequency characteristics of audio equipent, and mechanical vibrations. This paper is a report on the development of the exponential Laplace transform (ELT) techniquewhich has a unified form of both exponential and equal space sampling methods. This exponentialLaplace transform becomes identical to the conventional equal space sample Laplace transform.That is, the fast Laplace transform(= modified fast Fourier transform), if all the samples areequal spaced and it can be used that way too.

Since the accuracy of Laplace transform depends on the shifting constant, its selection criterion is clarified. The shifting constant was selected from the unit step and cosineresponses which are the basics for the ac and dc transient phenomena analysis. Sufficientaccuracies for practical applications were shown by comparing the computation results withthe exact solutions with samples of electric circuit transient phenomena. The exponentialLaplace transform is considered useful in transient phenomena analysis with wide frequencyand time ranges.

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Hiroshi Arita (Hitachi Research Laboratory, Hitachi Ltd.)
Akihiro Ametani (Faculty of Engineering, Doshisha University)

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