The input/output equation for an analog averager is given by the convolution integral

where x(t)is the input and y(t)the output.

(a) Change the above equation to determine the impulse response h(t).

(b) Graphically determine the output y(t) corresponding to a pulse input x(t) = u(t) ˆ’ u(t ˆ’ 2) using the convolution integral (let T = 1) relating the input and the output. Carefully plot the input and the output. (The output can also be obtained intuitively from a good understanding of the averager.)

(c) Using the impulse response h(t) found above, use now the Laplace transform to find the output corresponding to x(t) = u(t) ˆ’ u(t ˆ’ 2), let again T = 1 in the averager.

- кезаr У(0) — 1-T пр(1)х