This unique ECP experiment demonstrates fundamental properties of linear systems and dramatically illustrates the important principle of convolution. The properties of proportionality and superposition are first established via experimental measurement of system impulse responses. An oscillator is shown to superimpose the response of sequential impulses to constructively and destructively effect the output amplitude and phase.
These properties form the basis for the experimental demonstration of convolution and response to an arbitrary input. This experiment shows that an arbitrary continuous input function may be approximated by a series of discrete input impulses or steps. As the resolution of the series becomes fine, the output approaches that from the arbitrary input. Thus the experiment parallels the classical theoretical development of the convolution integral which is also included in the manual. Test results, shown in Figure 1, dramatically illustrate the convergence of the impulse series response to that of the continuous function.
This experiment is given in detail in the optional Dynamics package. It may also be performed using the basic Control Systems package and the versatile features of the Executive Interface program. This and other unique ECP experiments inspire an intuitive, hands-on understanding of important linear system principles.
