Digital Signal Processing Reference
In-Depth Information
4
2
0
0
0.2
0.4
0.6
0.8
1
(a) Frequency, Units of
π
4
2
0
0
0.2
0.4
0.6
0.8
1
(b) Frequency, Units of
π
Figure 3.4:
(a) 1000 samples of the
z
-transform
X(z)
of the sequence [1,1,1,1], obtained by direct
evaluation of the z-transform
X(z)
=1+
z
−
1
+
z
−
2
+
z
−
3
;(b) 1000 samples of the
z
-transform of the same
sequence, reconstructed from four samples of
X(z)
using Eq. (3.5).
2
1
0
−1
0
5
10
15
20
25
30
(a) n
2
1
0
−1
0
5
10
15
20
25
30
(b) n
Figure 3.5:
(a) A reconstruction of
x
= [1,1,1,1] from a reconstruction of
X(z)
based on six samples
of
X(z)
; (b) A reconstruction of a periodic version of
x
[
n
]
[
n
]
directly from the six samples of
X(z)
.
