Transfer behavior of linear systems, convolution and deconvolution

Abstract

The transfer behavior of a linear system can be described by its input and output signals and expressed in the time domain or frequency domain. In order to analytically determine the transfer behavior of a system, the Laplace transform of a time function into the complex variable domain (spectral domain, frequency domain) and the subsequent inverse transform into the time domain is a very effective tool. The step responses of simple RC and RCL circuits, which represent the basic elements of voltage dividers, shunts and measuring coils, are calculated using the Laplace transform. With the convolution integral, the output signals of the RC and RCL circuits are calculated for some characteristic input signals. This opens up a variety of possibilities to thoroughly analyze and optimize impulse voltage and current measuring systems and their components without the need for extensive experimental investigations. For calculations with experimental step responses, numerical convolution is applicable due to the high computing power of the PC as well as the significantly improved properties of digital recorders.