(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 ...)
 
Line 7: Line 7:
 
   </tr>
 
   </tr>
 
   <tr>
 
   <tr>
     <td>X0[n]=&delta;[n]</td><td>&nbsp;&nbsp;->&nbsp;&nbsp;</td><td>    Y0[n]=&delta;[n-1]</td>
+
     <td>X0[n]=&delta;[n]</td><td>&nbsp;&nbsp; &nbsp;&nbsp;</td><td>    Y0[n]=&delta;[n-1]</td>
 
   </tr>
 
   </tr>
 
   <tr>
 
   <tr>
     <td>X1[n]=&delta;[n-1]</td><td>&nbsp;&nbsp;->&nbsp;&nbsp;</td><td>    Y1[n]=4&delta;[n-2]</td>
+
     <td>X1[n]=&delta;[n-1]</td><td>&nbsp;&nbsp; &nbsp;&nbsp;</td><td>    Y1[n]=4&delta;[n-2]</td>
 
   </tr>
 
   </tr>
 
   <tr>
 
   <tr>
     <td>X2[n]=&delta;[n-2]</td><td>&nbsp;&nbsp;->&nbsp;&nbsp;</td><td>    Y2[n]=9 &delta;[n-3]</td>
+
     <td>X2[n]=&delta;[n-2]</td><td>&nbsp;&nbsp; &nbsp;&nbsp;</td><td>    Y2[n]=9 &delta;[n-3]</td>
 
   </tr>
 
   </tr>
 
   <tr>
 
   <tr>
     <td>X3[n]=&delta;[n-3]</td><td>&nbsp;&nbsp;->&nbsp;&nbsp;</td><td>    Y3[n]=16 &delta;[n-4]</td>
+
     <td>X3[n]=&delta;[n-3]</td><td>&nbsp;&nbsp; &nbsp;&nbsp;</td><td>    Y3[n]=16 &delta;[n-4]</td>
 
   </tr>
 
   </tr>
 
   <tr>
 
   <tr>
Line 22: Line 22:
 
   </tr>
 
   </tr>
 
   <tr>
 
   <tr>
     <td>Xk[n]=&delta;[n-k]</td><td>&nbsp;&nbsp;->&nbsp;&nbsp;</td><td>    Yk[n]=(k+1)^2 &delta;[n-(k+1)]</td>
+
     <td>Xk[n]=&delta;[n-k]</td><td>&nbsp;&nbsp; &nbsp;&nbsp;</td><td>    Yk[n]=(k+1)^{}2 &delta;[n-(k+1)]</td>
 
   </tr>
 
   </tr>
 
</table>
 
</table>
 
For any non-negative integer k
 
For any non-negative integer k

Revision as of 14:19, 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

Alumni Liaison

Have a piece of advice for Purdue students? Share it through Rhea!

Alumni Liaison