142 2.22. For each of the following pairs of waveforms, use the convolution integral to find the response y(t) of the LTI system with impulse response h(1) to the input x(t).

Sketch your results. (a) -ar x(t) = e 'u(t) h(t) = e -Blu(1) (Do this both when a # ß and when a = B.) (b) x(t) = u(t) - 2u(t-2) + u(t - 5) h(t) = e²u(1-1) (c) x(t) and h(t) are as in Figure P2.22(a). (d) x(1) and h(t) are as in Figure P2.22(b). (e) x(1) and h(t) are as in Figure P2.22(c). Linear Time-Invariant Systems Chap. 2