Consider a continuous-time LTI system for which the input x(t) and output y(t) are relat...

Consider a continuous-time LTI system for which the input x(t) and output y(t) are related by the differential equation

Let X(s) and Y(s) denote Laplace transforms of x(t) and y(t), respectively, and let H(s) denote the Laplace transform of h(t), the system impulse response.

(a) Determine H(s) as a ratio of two polynomials in s. Sketch the pole-zero pattern of H(s).

(b) Determine h(t) for each of the following cases:

1. The system is stable.

2. The system is causal.

3. The system is neither stable nor causal.