A single input-output relationship is given for each of the following three systems:
(a) System A: x[n] = (1/3)n, y[n] = 2(1/3)n.
(b) System B: x[n] = (1/2)n, y[n] = (1/4)n.
(c) System C: x[n] = (2/3)nu[n], y[n] = 4(2/3)nu[n] – 3(1/2)nu[n].
Based on this information, pick the strongest possible conclusion that you can make about each system from the following list of statements:
(i) The system cannot possibly be LTI.
(ii) The system must be LTI.
(iii) The system can be LTI, and there is only one LTI system that satisfies this input-output constraint.
(iv) The system can be LTI, but cannot be uniquely determined from the information in this input-output constraint.
If you chose option (iii) from this list, specify either the impulse response h[n] or the frequency response H(ejω) for the LTI system.