(New page: == Part A == BLECK == Part B == LAWL) |
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| − | == Part A == | + | == Part A: Can the system be time invariant? == |
| − | + | The system cannot be time invariant. | |
| + | |||
| + | |||
| + | For instance, the input | ||
| + | |||
| + | <math>\,X_0[n]=\delta [n]\,</math> | ||
| + | |||
| + | yields the output | ||
| + | |||
| + | <math>\,Y_0[n]=\delta [n-1]\,</math> | ||
| + | |||
| + | Thus, | ||
| + | |||
| + | <math>\,Y_0[n-1]=\delta [n-2]\,</math> | ||
| + | |||
| + | |||
| + | However, the input | ||
| + | |||
| + | <math>\,X_0[n-1]=\delta [n-1]=X_1[n]\,</math> | ||
| + | |||
| + | yields the output | ||
| + | |||
| + | <math>\,Y_1[n]=4\delta[n-2]\,</math> | ||
| + | |||
| + | |||
| + | Since these two are not equal | ||
| + | |||
| + | <math>\,\delta [n-2]\not= 4\delta[n-2]\,</math> | ||
| + | |||
| + | the system is time variant (by not fitting the definition of time invariance). | ||
== Part B == | == Part B == | ||
LAWL | LAWL | ||
Revision as of 19:28, 11 September 2008
Part A: Can the system be time invariant?
The system cannot be time invariant.
For instance, the input
$ \,X_0[n]=\delta [n]\, $
yields the output
$ \,Y_0[n]=\delta [n-1]\, $
Thus,
$ \,Y_0[n-1]=\delta [n-2]\, $
However, the input
$ \,X_0[n-1]=\delta [n-1]=X_1[n]\, $
yields the output
$ \,Y_1[n]=4\delta[n-2]\, $
Since these two are not equal
$ \,\delta [n-2]\not= 4\delta[n-2]\, $
the system is time variant (by not fitting the definition of time invariance).
Part B
LAWL
