New algorithm of numerical inversion of D-transform

New algorithm of numerical inversion of D-transform

Článek recenzovaný mimo WoS a Scopus

The D-transform, introduced in 1998 by J. Hekrdla, converts a continuous-time signal to a sequence. In contrast to the classical sampling, there is no such visible connectivity between the continuous-time signal and its discrete-time counterpart in the time domain. The main feature of the D-transform consists in preserving the relations between the derivative of continuous-time signal and the difference of discrete-time signal. This fact enables, among other things, changing the problem of numerical solution of differential equations into the simpler problem of solving difference equations, without losing accuracy. The inverse D-transform represents a pending issue because it cannot be derived in closed form as in the case of the Fourier, Laplace, or other known transforms. This paper describes a novel method of D-transform inversion, which is based on mutual correspondence between the D-, z-, and Laplace transforms. Numerical accuracy is provided by the algorithm of the inverse Laplace transform, which works reliably also in the case of periodical or divergent signals.

The D-transform, introduced in 1998 by J. Hekrdla, converts a continuous-time signal to a sequence. In contrast to the classical sampling, there is no such visible connectivity between the continuous-time signal and its discrete-time counterpart in the time domain. The main feature of the D-transform consists in preserving the relations between the derivative of continuous-time signal and the difference of discrete-time signal. This fact enables, among other things, changing the problem of numerical solution of differential equations into the simpler problem of solving difference equations, without losing accuracy. The inverse D-transform represents a pending issue because it cannot be derived in closed form as in the case of the Fourier, Laplace, or other known transforms. This paper describes a novel method of D-transform inversion, which is based on mutual correspondence between the D-, z-, and Laplace transforms. Numerical accuracy is provided by the algorithm of the inverse Laplace transform, which works reliably also in the case of periodical or divergent signals.

D-transform, s-z correspondence, continuous-time signal, discrete-time signal

D-transform, s-z correspondence, continuous-time signal, discrete-time signal

BIOLEK, D.; BIOLKOVÁ, V.; KOLKA, Z.

01.01.2007

WSEAS

Greece

1790-5022

3

1

38

43

6