Digital Signal Processing Reference
In-Depth Information
which results in Fig. 2.7. Theoretically, any counterclockwise closed contour in the ROC will result in
the same answer; circular contours are particularly easy to specify and compute. You can verify that any
circular contour in the ROC will give the same answer by changing the value of
ContourRad.
1
0.5
0
−0.5
−1
0
10
20
30
40
50
(a) n
1
0.5
0
−0.5
−1
0
10
20
30
40
50
(b) n
Figure 2.7:
(a) The real part of the first 50 samples of the impulse response corresponding to the
z
-
transform 1/(1 -1.2
z
−
1
+0
.
81
z
−
2
), computed using numerical contour integration along a circular contour
of radius 1.0 since the largest magnitude pole is 0.9; (b) Imaginary part of same.
Example 2.28.
Estimate, using numerical contour integration, the time domain sequence corresponding
to the
z
-transform
z
−
1
X(z)
=
(
ROC:
|
z
|
>
1
.
0
)
−
2
z
−
1
+
z
−
2
1
We make the call
LVxNumInvZxform([0,1],[1,-2,1],10000,1.05,[0:1:50])
which results in Fig. 2.8.
The call immediately above yields the sequence
x
[
n
]=
nu
[
n
]
