(a) Compute the convolution of each of the following pairs of signals x(t) and h(t) by
Chapter 4, Problem 4.26(choose chapter or problem)
(a) Compute the convolution of each of the following pairs of signals x(t) and h(t) by calculating X(jw) and H(jw ), using the convolution property, and inverse transforming. (i) x(t) = te-lt u(t), h(t) = e-4t u(t) (ii) x(t) = te-lt u(t), h(t) = te-4t u(t) (iii) x(t) = e-tu(t), h(t) = etu(-t) (b) Suppose that x(t) = e-(t-l)u(t- 2) and h(t) is as depicted in Figure P4.26. Verify the convolution property for this pair of signals by showing that the Fourier transform of y(t) = x(t) * h(t) equals H(jw )X(jw ).
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