An input signal x (t) = u(t-1)-u(t-3) is applied to an LTI system h (t) = 8(t-2) to give the output y (t). a) (2) Sketch x(t) and h (t). Show important values. b) (2) Use convolution integral to express the output y (t) in terms of h (t) only. c) (2) Write down the output expression and sketch the output y (t). Show important values. The output y (t) is then applied to a differentiator to give z (t). d) (2) Write down the expression of z (t) and sketch z (t). Show important values. The input signal x (t) is applied to an LTI system h(t) = u(t-2) - u(t-6) to give the output y (t). e) (2) Sketch the output y (t). Show important values. The input signal x (t) is applied to an LTI system h3 (t) = -1 h (t-2k) to give the output y3 (t). f) (2) Sketch the output y3 (t). Show important values. The output y(t) is then applied to an integrator to give z3(t). g) (2) Sketch Z3 (t). Show important values. The block diagram of an LTI system ho(t) is given below. x(t) h (t) d dt h (t) y(t) ho(t) h) (2) Write down the impulse response of the overall LTI system in terms of h (t) and h (t). The input signal x (t) is applied to the LTI system h, (t) shown above to give the output y(t). i) (2) Sketch the output y(t). Show important values. j) (2) Write down the expression of y(t).