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**LTI/Impulse Response: URGENT**

**1. Following single input-output relations are given for 3 systems**

System A: x[n] = (1/2)^n; y[n] = (1/4)^n

System B: x[n] = cos (pi/3 n); y[n] = 3j Sin (pi/3 n)

System C: x[n] = (1/5) * (1/5)^n * u[n] ; y[n] = -b * (1/2)^n * u[-n-1] - b * (1/3)^n * u[n]

where * denoted multiplication

Based on this data, choose for each system

1) System Must be LTI and is uniquely specified by the information

2) system must be LTI but cannot be uniquely determined

3) system could be LTI and if it is, it can be uniquely specified

4) system could be LTI but cannot be determined uniquely

5) system is not LTI

if you choose 1) or 3) then specify the impulse response h[n]

System A: x[n] = (1/2)^n; y[n] = (1/4)^n

System B: x[n] = cos (pi/3 n); y[n] = 3j Sin (pi/3 n)

System C: x[n] = (1/5) * (1/5)^n * u[n] ; y[n] = -b * (1/2)^n * u[-n-1] - b * (1/3)^n * u[n]

where * denoted multiplication

Based on this data, choose for each system

1) System Must be LTI and is uniquely specified by the information

2) system must be LTI but cannot be uniquely determined

3) system could be LTI and if it is, it can be uniquely specified

4) system could be LTI but cannot be determined uniquely

5) system is not LTI

if you choose 1) or 3) then specify the impulse response h[n]

**2. The attempt at a solution:**

First is easy, as it is not LTI.

Don't know what to do with second and thrid part

First is easy, as it is not LTI.

Don't know what to do with second and thrid part