Question

Given the signals x(t)=(t+1)[u(t+1)-u(t)]+(-t+1)[u(t)-u(t-1)] and h(t)=u(t+3)-u(t-3), find the convolution y(t)=x(t)•h(t):

Answer 1

Let us expand the x(t) given and write into a simplified formwe know that any signal which is convoluted with unit step signal would give the integral of the signal. So here the ramp terms become parabolic terms after convolution with the step terms. The time shifting gets added as shown. We can write the parabolic signals in terms of unit step terms as given.

Hence we have the answer.