PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

478 Practical MATLAB® Applications for Engineers

Recall that if

Hz

Gz

Fz

A

az

Az

za

()

()

() ()










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)

. (^) H 1 (z)H 2 (z)
h 1 (n) ↔ H 1 (z) h 2 (n) ↔ H 2 (z)
H1(z)H2(z)
FIGURE 5.14
System diagram of R.5.57.
f(n) ↔ F(z) h(n) ↔ H(z) g(n) ↔ G(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.
Zfn Fz fnzn
n

[()]

() ()





∞

∑

Hz hnzn

n

()
( )

 



∑