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Let us apply a time-delay of <math>n_0</math> to the system. | Let us apply a time-delay of <math>n_0</math> to the system. | ||
| − | <math>\delta[n - k] \rightarrow system \rightarrow (k + 1)^2 \delta[n - (k + 1)] \rightarrow time-delay \rightarrow (k + 1)^2 \delta[n - n_0 -(k + 1)] </math> | + | <math>\delta[n - k] \rightarrow system \rightarrow (k + 1)^2 \delta[n - (k + 1)] \rightarrow time-delay \rightarrow (k + 1)^2 \delta[n - n_0 -(k + 1)] = (k + 1)^2 \delta[n -(k + 1 -n_0)] </math> |
Revision as of 15:40, 11 September 2008
6 a) The system cannot be time-invariant.
$ X_k[n] = \delta[n - k] \rightarrow system \rightarrow Y_k[n] = (k + 1)^2 \delta[n - (k + 1)] $
Let us apply a time-delay of $ n_0 $ to the system.
$ \delta[n - k] \rightarrow system \rightarrow (k + 1)^2 \delta[n - (k + 1)] \rightarrow time-delay \rightarrow (k + 1)^2 \delta[n - n_0 -(k + 1)] = (k + 1)^2 \delta[n -(k + 1 -n_0)] $
