QUESTION 4
(a) Suppose an LTIC system has an impulse response h(t) and input impulse-train signal x(t)=\delta _(T_(0))(t)=\sum_(n=-\infty )^(\infty ) \delta (t-nT_(0)) depicted in Figure Q4(a), respectively.
(i) Given that the convolution of m(t) and g(t) is by definition of the form m(t)**g(t)=\int_(-\infty )^(\infty ) m(\tau )g(t-\tau )d\tau , show that \delta (t-T_(0))**g(t)=g(t-T_(0)).
[4 Marks]
(ii) Hence, use the result in (i) to determine and sketch y(t)=x(t)**h(t) for T_(0)=3 with respect to Figure Q4(a).
[6 Marks]
(b) For the LTIC system depicted in Figure Q4(b), use time domain analysis to determine the response voltage v(t) for 0<=t<\infty , given that the initial energy is zero.
[10 Marks]
