A Systematic Approach to the Time-Domain Computation of the Impulse Response and Post-Initial Conditions of Causal LTI Systems at the Origin

摘要

This paper presents a systematic approach to the computation of the impulse response in the time domain at the origin and post-initial conditions of an N~(th)-order causal SISO LTI system differential equation. It is shown that the solution and its N-1 derivatives of such a differential equation with a unit impulse input in the time interval 0~- ≤ t ≤ 0~+ are singularity functions, each containing one stepwise discontinuity term whose magnitude is one of the N post-initial conditions of the differential equation for t ≥ 0~+. The approach presented is envisaged to provide a simplified tool not only for the computation but also for the teaching of the impulse response.