Suppose that S is an LTI system whose exact form is unknown. It is tested by running some inputs into the system, and then observing the output signals. Suppose that the following input-output pairs are the result of the tests:

(a) Make a plot of the signal

(b) Use linearity and time invariance to find the output of the system when the input is

Input: x[n] Output: y[n] [n] [n 1] | 5[n]- [n 1] + 25[n 3] COS(n/2) 2 os(n/2 - /4) y[n] = 8[n] 8[n 1] + 28[n-3]. - x[n] = 78[n] - 78[n - 2]