An analog averager is given by (a) Let x(t) = u(t) u(t 1) find the average signal y(t) using the above integral. Let T =

An analog averager is given by

(a) Let x(t) = u(t) ˆ’ u(t ˆ’ 1) find the average signal y(t) using the above integral. Let T = 1. Carefully plot y(t). Verify your result by graphically computing the convolution of x(t) and the impulse response h(t) of the averager.

(b) To see the effect of the averager, consider the signal to be averaged to be x(t) = cos(2Ï€ t/T₀) u(t), select the smallest possible value of Tin the averager so that the steady state response of the system, y(t) as t †’ ˆž, will be 0.

(c) Use MATLAB to compute the output in part (b). Compute the output y(t) for 0 ‰¤ t ‰¤ 2 at intervals T_s = 0.001. Approximate the convolution integral using the function conv(use help to find about conv) multiplied by T_s.

y(t) t-T