Numerical Laplace Transformation and Inversion using Fast Fourier Transform

Abstract

The Laplace transform is known as one of the most useful mathematical tools for solving a wide range of engineering problems. For its application to theoretical or numerical analyses, methods of numerical inversion have been studied extensively. On the other hand, the method of numerical transformation has not yet been studied very much. This is one of the reasons why few applications of the Laplace transform to experimental analysis have been reported. In the present paper, a method for numerical Laplace transformation and inversion utilizing the fast Fourier transform (FFT) algorithm is studied with the intention of applying it to experimental analysis. A discrete Laplace transform pair is formulated as in the discrete Fourier transform pair. The numerical accuracy of the present method is evaluated for the sinusoidal function and step function. A chart is presented for determining parameters for computation so as to attain a specified accuracy.