(New page: == Part E. Linearity and Time Invariance == A discrete-time system is such that when the input is one of the signals in the left column, then the output is the corresponding signal in the ...) |
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</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td>X0[n]=δ[n]</td><td> | + | <td>X0[n]=δ[n]</td><td> </td><td> Y0[n]=δ[n-1]</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td>X1[n]=δ[n-1]</td><td> | + | <td>X1[n]=δ[n-1]</td><td> </td><td> Y1[n]=4δ[n-2]</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td>X2[n]=δ[n-2]</td><td> | + | <td>X2[n]=δ[n-2]</td><td> </td><td> Y2[n]=9 δ[n-3]</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td>X3[n]=δ[n-3]</td><td> | + | <td>X3[n]=δ[n-3]</td><td> </td><td> Y3[n]=16 δ[n-4]</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 22: | Line 22: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td>Xk[n]=δ[n-k]</td><td> | + | <td>Xk[n]=δ[n-k]</td><td> </td><td> Yk[n]=(k+1)^{}2 δ[n-(k+1)]</td> |
</tr> | </tr> | ||
</table> | </table> | ||
For any non-negative integer k | For any non-negative integer k | ||
Revision as of 13:19, 11 September 2008
Part E. Linearity and Time Invariance
A discrete-time system is such that when the input is one of the signals in the left column, then the output is the corresponding signal in the right column:
| Input | Output | |
| X0[n]=δ[n] | Y0[n]=δ[n-1] | |
| X1[n]=δ[n-1] | Y1[n]=4δ[n-2] | |
| X2[n]=δ[n-2] | Y2[n]=9 δ[n-3] | |
| X3[n]=δ[n-3] | Y3[n]=16 δ[n-4] | |
| ... | ... | |
| Xk[n]=δ[n-k] | Yk[n]=(k+1)^{}2 δ[n-(k+1)] |
For any non-negative integer k
