Digital Signal Processing Reference
In-Depth Information
zplane(z, p)
where
z
and
p
are column vectors of zeros and poles of the transfer function, or, alternately
zplane(b, a)
where
b
and
a
are row vectors of the
z
-transform numerator and denominator coefficients, respectively.
The m-code used to generate Fig. 2.3 was
freq = -pi:0.02:pi;z=exp(j*freq);
FR = abs(1 + z.ˆ(-4));
figure(44); subplot(211);
plot(freq/pi,FR)
xlabel('Frequency, Units of
π
)
ylabel('Magnitude')
subplot(212);
zplane([10001],1)
xlabel('Real Part')
ylabel('Imaginary Part')
2.5
2
1.5
1
0.5
0
−1
−0.5
0
0.5
1
(a) Frequency, Units of
π
1
0.5
4
0
−0.5
−1
−4
−3
−2
−1
0
1
2
3
4
(b) Real
Figure 2.3:
(a) Magnitude of the
z
-transform of a unity-additive comb filter having a delay of four
samples, having the
z
-transform
H(z)
=1+z
−
4
; (b) Plot of the zeros of the
z
-transform of the comb
filter of (a). Note the four poles at
z
=0.
For more complicated transfer functions, the roots can be found using the function
roots
.
Example 2.17.
Obtain the z-transform and its roots for the finite impulse response
[
1
,
0
,
0
,
0
,
0
.
5
]
.
