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The unit impulse response:
The response of a system to the unit impulse is of importance, for as we shall show below, it characterizes the LSI system completely. Let us consider the following system and calculate the unit step response to it: y[n] = x[n] - 2x[n-1] + 3x[n-2]. Now, we apply a unit step x[n]=d[n] to the system and calculate the response :
|
 |
|
n |
x[n] |
x[n-1] |
x[n-2] |
y[n] |
|
..., -1 |
0 |
0 |
0 |
0 |
|
0 |
1 |
0 |
0 |
1 |
|
1 |
0 |
1 |
0 |
-2 |
|
2 |
0 |
0 |
1 |
3 |
|
3, ... |
0 |
0 |
0 |
0 |
The graphical calculation and the response are as follows :
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