Digital Signal Processing Reference
In-Depth Information
4
2
0
1
−2
−4
0
0
10
20
30
40
50
60
−1
(b) Sample Number of Real Output
4
0
20
40
60
2
(a) Sample Number of Input
0
−2
+
−4
Input (Real)
0
10
20
30
40
50
60
(c) Sample Number of Imaginary Output
0.53
−0.52
−0.47
1
0.5
0
0.9
−0.5
−1
−1
0
1
Magnitude
Angle(Degrees)
(d) Real
Figure 4.36:
(a) Input sequence, a chirp; (b) Real part of output sequence, showing a lowpass effect;
(c) Imaginary part of output sequence, identically zero; (d) The pole, plotted in the complex plane.
1
,p,p
2
,p
3
, ...
and
1
,p
c
,p
c
,p
c
, ...
where
p
c
is the complex conjugate of
p
. The first few terms of the convolution are
1
p
+
p
c
p
2
p
c
+
pp
c
+
p
3
p
2
p
c
+
pp
c
+
p
c
+
(4.22)
