(New page: == Time invariant == <math> X_k[n] = \delta[n-k] \!</math> <math> \delta[n-k] --> System --> Y_k[n] --> Time Shift --> (k + 1)^2\delta[n - (k + 1 + n_o)]\!</math> <math>\delta[n-k] -->...) |
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Latest revision as of 12:50, 12 September 2008
Time invariant
$ X_k[n] = \delta[n-k] \! $
$ \delta[n-k] --> System --> Y_k[n] --> Time Shift --> (k + 1)^2\delta[n - (k + 1 + n_o)]\! $
$ \delta[n-k] --> Time Shift --> \delta[n-k-n_o] --> System --> (k + 1 + n_o)^2\delta[n - (k + 1 + n_o)]\! $
The System is Time Variant because:
$ (k + 1)^2\delta[n - (k + 1 + n_o)] \neq (k + 1 + n_o)^2\delta[n - (k + 1 + n_o)]\! $
Linear
Since it is stated that the system is linear we can look up the table to see what Input leads to an output of $ Y[n] = u[n-1] $
According to the table, the input $ X_o[n] = \delta[n] $ gives us the output $ Y[n] = u[n-1] $
