Digital Signal Processing Reference
In-Depth Information
w = 0:0.01:pi; DTF T = 1./(1-0.9*exp(-j*(w)));
figure(8); plot(w/(pi),abs(DTF T));
xlabel('Normalized Frequency'); ylabel('Magnitude')
Example 1.2.
Evaluate and plot the magnitude of the DTFT of the following sequence:
[
1
,
0
,
1
]
.
2
e
−
jωn
e
−
jω
0
,e
−
jω
1
,e
−
jω
2
e
−
jω
2
F(ω)
=
x
[
n
]
=
[
1
,
0
,
1
][
]=
1
+
(1.6)
n
=
0
From our earlier work, we recognize the impulse response [1,0,1] as that of a simple bandstop
filter. We can show that this is so by evaluating Eq. (1.6) at a large (but necessarily finite) number of
values of
ω
with the following code, the results of which are shown in Fig. 1.1.
w = 0:0.01:pi; DTF T = 1+exp(-j*2*w);
figure(8); plot(w/(pi),abs(DTF T));
xlabel('Normalized Frequency'); ylabel('Magnitude')
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
Normalized Frequency
Figure 1.1:
Magnitude of the DTFT of the simple notch filter [1, 0, 1].
