1. (a) Consider a linear and time-invariant (LTI) system with the impulse response h(t) as shown in Figure 1: -2 h(t) 2 5 Figure 1 Further denote the input and the output of the LTI system as x(t) and y(t), respectively. Answer each of the following questions and express your answer in equation. No need to plot your answer. (i) If y(t) h(t), find the input signal x(t). Note: Question No. 1 continues on page 2. 1 (ii) Find the unit-step response s(t). (iii) If x(t)=3u(t+3)-4u(t-5), find the output y(t) and express it in terms of the unit-step response s(t). (iv) If x(t)=h(t), find the output y(t). (15 Marks) (b) Determine whether the given LTI system in part (a) is memoryless, causal, and bounded-input-bounded-output stable. Justify each property you claim. (6 Marks) (c) Sketch the even part and the odd part of h(t) given in Figure 1 on page 1 seperately. (4 Marks)