Problem 1

We are given a certain linear time - invariant system with impulse response . We are told that when the input is the output is , which is sketched in figure below. We are then given the following set of inputs to linear time - invariant systems with the indicated impulse responses:  

	Input x(t)	Impulse response h(t)
(a)
(b)
(c)
(d)
(e)
(f)

[Here and denote the first derivative of and , respectively.]

In each of these cases, determine whether or not we have enough information to determine when the input is and the system has impulse response . If it is possible to determine , provide an accurate sketch of it with numerical values clearly indicated on the graph.