Obtain and sketch the convolutions of the following signals. (a) y 1 (t) = e -at u(t)

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Obtain and sketch the convolutions of the following signals.

(a) y1(t) = e-atu(t) ∗ Il(t - τ), a and τ positive constants

(b) y2(t) = [II(t/2) + II(t)] ∗ Il(t)

(c) y3(t) = e-α|t| ∗ II(t), a > 0 

(d) y4 (t) = x(t) ∗ u (t), where x(t) is any energy signal [you will have to assume a particular form for x(t) to sketch this one, but obtain the general result before doing so].

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