Perform convolutions of the following functions, specifying the solution analytically and also sketching them by hand....

 

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Perform convolutions of the following functions, specifying the solution analytically and also sketching them by hand. Be aware that you may be able to compute some answers from other answers through use of convolution properties. (a) x(t) = e²tu(t) and h(t) = e-tu(t) (b) x(t) = = e -2tu(t) and h(t) = e−(t-¹)u(t – 1) (c) x(t) = rect(t + 1/2) and h(t) = rect(t/2) (Recall rect(t) is the rectangular pulse defined by rect (t) = u(t + 1/2) – u(t-1/2)) (d) x(t) = e-2tu(t) and h(t) = rect(2t) (e) x(t) = e-²tu(t) and h(t) = e-tu(t) + rect(2t) (f) x(t) = at +b and h(t) rect(t - 1/2) = Perform convolutions of the following functions, specifying the solution analytically and also sketching them by hand. Be aware that you may be able to compute some answers from other answers through use of convolution properties. (a) x(t) = e²tu(t) and h(t) = e-tu(t) (b) x(t) = = e -2tu(t) and h(t) = e−(t-¹)u(t – 1) (c) x(t) = rect(t + 1/2) and h(t) = rect(t/2) (Recall rect(t) is the rectangular pulse defined by rect (t) = u(t + 1/2) – u(t-1/2)) (d) x(t) = e-2tu(t) and h(t) = rect(2t) (e) x(t) = e-²tu(t) and h(t) = e-tu(t) + rect(2t) (f) x(t) = at +b and h(t) rect(t - 1/2) =

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a For the convolution of xt and ht we can calculate it analytically using the integral xt ht 0 to t ... View the full answer