Question: A linear time-invariant system has impulse response: h(t) = e(t - 2) u(t - 2)
(a) Plot h(t - τ) versus τ, for t = 1. Label your plot.
(b) Is the LTI system causal? Give a reason to support your answer.
(c) Is the system stable? Explain with a proof or counter example.
(d) If the input is x(t) = u(t), then it will be true that the output y(t) is zero for t ≤ t1. Find t1
(e) The rest of the output signal (for t > t1) is nonzero when the input is x(t) = u(t). Use the convolution integral to find the nonzero portion of the output; i.e., find y(t) for t > t1.