478
Practical MATLAB
® Applications for Engineers
Recall that if
H z
G z
F z
A
a z
Az
z a
( )
( )
( )
( )
ϭ
ϭ Ϫ
ϭ Ϫ
Ϫ
1
1
then the ROC is given by |z| > |a|, where a may be real or complex. The ROC is revisited
later in this chapter.
R.5.56 Simple-system structures consisting of two cascaded blocks are analyzed in the
time domain and z-domain (frequency), in Figures 5.12 and 5.13, respectively.
FIGURE 5.12
System-time block diagram of R.5.56.
f(n)
f(n)
h 1 (n)
h 2 (n)
g(n) = h 1 (n) ⊗ h 2 (n) ⊗ f(n)
g(n) = h 1 (n) ⊗ h 2 (n) ⊗ f(n)
h 1 (n) ⊗ h 2 (n)
FIGURE 5.13
System block diagram in the z-domain of R.5.56.
f(n) ↔ F(z)
g(n) ↔ G(z)
F(z)
G(z) = F(z) . H1(z)H2(z)
h1(n) ↔ H1(z)
h2(n) ↔ H2(z)
H1(z)H2(z)
FIGURE 5.14
System diagram of R.5.57.
f(n) ↔ F(z)
g(n) ↔ G(z)
h(n) ↔ H(z)
ANALYTICAL Solution
R.5.57 Let us revisit the simple system shown in Figure 5.14 and review the relations
between the time and z-domains.
Z f n
F z
f n z
n
n
[ ( )]
( )
( )
ϭ
ϭ
Ϫ
ϭϪ
ϩϱ
∞
∑
H z
h n z
n
n
( )
( )
ϭ
Ϫ
ϭϪϱ
ϩϱ
∑
CRC_47760_CH005.indd 478
CRC_47760_CH005.indd 478
7/23/2008 1:47:22 PM
7/23/2008 1:47:22 PM