Problem

Suppose that is an LTI system whose exact form is unknown. It has been tested by observin...

Suppose that is an LTI system whose exact form is unknown. It has been tested by observing the output signals corresponding to several different test inputs. Suppose that the following input–output pairs were the result of the tests:

Input: x[n]	Output: y[n]
δ[n]	δ[n] − δ[n − 3]
cos(2πn/3)	0
cos(πn/3 + π/2)	2 cos(πn/3 + π/2)

(a) Make a plot of the signal x[n] = 3δ[n] − 2δ[n −2] + δ[n − 3].
(b) When the input is x[n] = 3δ[n] − 2δ[n − 2] + δ[n − 3], determine the output of the system and make a plot of it.
(c) Determine the output when the input is x[n] = cos(π(n − 3)/3).
(d) Is the following statement true or false? Explain.