Question: Use linearity and time invariance to determine the step response of a system whose impulse response is the following rectangular pulse:
h(t) = 5u(t - 1) - 5u(t - 4)
(a) Expand the convolution into two terms and exploit the result from Example to get y(t) u(t)* h(t).
(b) Write the answer for y(t)as separate cases over three different regions of the time axis.
(c) Make a plot of y(t) versus t.
Example: Convolve Unit steps
When the impulse response is unit step, h(t) = u(t) and the input is also a unit step, x(t) = u(t), the convolution integral becomes
