Digital Signal Processing Reference
In-Depth Information
Another script
LV xP lotZT ransf ormMag(ZeroV ec, P oleV ec, rMin, rMax, NSamps)
will take arguments as a row vector of zeros (
ZeroVec
), a row vector of poles (
PoleVec
), the minimum
radius contour to compute (
rMin
), the maximum radius contour to compute (
rMax
), and the number of
frequency samples along each contour to compute,
NSamps
. By passing both
rMin
and
rMax
as 1, the
standard frequency response can be obtained.
A call to solve the current example would be
LVxPlotZTransformMag([],[(0.5 + 0.85*j),(0.5 - 0.85*j)],1,1,256)
which results in Fig. 2.20.
35
30
25
20
15
10
5
0
1
0.5
−1
−0.5
0
0
−0.5
0.5
−1
1
Imaginary
Real
Figure 2.20:
Magnitude of
z
-transform of the IIR formed from the poles (0.5 + 0.85j) and (0.5 - 0.85j)
,
evaluated along the unit circle.
Example 2.41.
Evaluate the frequency response of the
z
-transform below at radian frequency
π/
4, and
then obtain the impulse response for the first 150 samples, correlate it with the complex exponential
corresponding to the same radian frequency (i.e., compute the CZL), and compare the correlation value
to the answer obtained directly from the
z
-transform. The z-transform is
1
X(z)
=
0
.
9
z
−
1
1
−
