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Problems 291
x(n)
−1/2
1/2
−2/3
0.56
2/3
−0.56
z −1 z −1 z −1
y(n)
FIGURE P6.2 Structure for Problem 6.9
P6.9 Figure P6.2 describes a causal linear time-invariant system. Determine and draw the
following structures:
1. Direct form I
2. Direct form II
3. Cascade form containing second-order direct-form-II sections
4. Parallel form containing second-order direct-form-II sections
P6.10 A linear time-invariant system with system function
H(z) =
0.05 − 0.01z −1 − 0.13z −2 +0.13z −4 +0.01z −5 − 0.05z −6
1 − 0.77z −1 +1.59z −2 − 0.88z −3 +1.2z −4 − 0.35z −5 +0.31z −6
is to be implemented using a flow graph of the form shown in Figure P6.3.
1. Fill in all the coefficients in the diagram.
2. Is your solution unique? Explain.
x(n)
z −1
z −1
z −1
z −1
y(n)
z −1
z −1
z −1
z −1
FIGURE P6.3 Structure for Problem 6.10
P6.11 A linear time-invariant system with system function
H(z) = 0.051+0.088z−1 +0.06z −2 − 0.029z −3 − 0.069z −4 − 0.046z −5
1 − 1.34z −1 +1.478z −2 − 0.789z −3 +0.232z −4
is to be implemented using a flow graph of the form shown in Figure P6.4. Fill in all the
coefficients in the diagram.
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