An example is presented in this page, where the input is a time-shifted or a delayed pulse. This page makes use of the results obtained in the previous page. As before, both the functions, h(t) and f(t), are pulses.
Given the two waveforms shown in Fig. 19, obtain the convolution integral of h(t) and f(t). Let
y(t) = f(t) * h(t).
SOLUTION :
Convolution Integral Approach: Analytical Technique
In the previous page, the given functions are h(t) and g(t), the convolution integral of h(t) and g(t) has been obtained and it is presented as z(t) in Fig. 20. It turns out that f(t) is a delayed pulse, similar to g(t). The convolution integral z(t) can be obtained as shown below.
Since f(t) is a delayed pulse, we get the equation (5.2).
From equations (5.1) and (5.2), we can obtain y(t) from z(t) , by replacing t by ( t - 1).
Given a shifted or a delayed input function, the convolution integral can first be obtained, by ignoring the time delay. Then the response can be delayed corresponding to the delay in the input function . A few more examples are presented in the subsequent pages.