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Consider the system with following input-output relation \(y\left[ n \right] = \left[ {1 + {{\left( { - 1} \right)}^n}} \right]x\left[ n \right]\) where, x[n] is the input and y[n] is the output. The system is

Consider the system with following input-output relation \(y\left[ n \right] = \left[ {1 + {{\left( { - 1} \right)}^n}} \right]x\left[ n \right]\) where, x[n] is the input and y[n] is the output. The system is Correct Answer non-invertible and time varying

Given that, y = (1 + (-1)n) x

y = x        ----(1)

y = (1 + (-1)n) x       ----(2)

Both the equations 1 and 2 are not equal. Hence y is dependent on time. It is time variant.

For invertible systems, for each unique input x, there should be unique output y.

If x = δ

y = (1 + (-1)n) δ

y = 0

If x = k δ

y = k δ

y = 0

Hence for the two different inputs, system producing same output. Hence system is non invertible.

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