Introduction of the digital signal processing methodology (DSPM) for time integration

Abstract

Although the existence of a close relationship between the areas of digital signal processing and time integration methodology is known, a systematic application of the concepts and methods of the first area to the second is missing. Such an approach is followed in this paper, arising from the fact that any time integration formula can be viewed as a digital filter of the applied excitation force, approximating as close as possible to the behaviour of a ‘prototype analogue filter’, which is in fact the semi discrete equations of motion of the system. This approach provides a universal framework for handling and analysing all various aspects of time integration formulae, such as analysis in the frequency domain, algebraic operations, accuracy and stability, aliasing, spurious oscillations generation, introduction of digital filters within the time integration formula, initial conditions handling and overshooting. Additionally it is shown that digital signal processing methods, such as pre‐ or post‐processing, time delays, etc. can be in certain cases a quite effective complement of the time integration scheme.