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Problems 293
0.5
1
−1
z −1
2
1
z −1
3
−0.9
z −1
1.5
−0.8
z −1
x(n)
−0.5
z −1
1
2
−0.4
z −1
3
−0.5
y(n)
−0.5
z −1
1
−0.4
z −1
2
0.4
z −1
FIGURE P6.6 Structure for Problem 6.13
3. cascade form structure containing 2nd-order sections,
4. parallel form structure containing 2nd-order sections.
P6.14 In filter structure shown in Figure P6.7, systems H 1(z) and H 2(z) are subcomponents of a
larger system H(z). The system function H 1(z) isgiven in the parallel form
0.2 − 0.3z −1
H 1(z) =2+
1+0.9z −1 +0.9z + 0.4+0.5z −1
−2 1 − 0.8z −1 +0.8z −2
and the system function H 2(z) isgiven in the cascade form
(
)(
)
2+z −1 − z −2 3+4z −1 +5z −2
H 2(z) =
1+1.7z −1 +0.72z −2 1 − 1.5z −1 +0.56z −2
1. Express H(z) asarational function.
2. Draw the block diagram of H(z) asacascade-form structure.
3. Draw the block diagram of H(z) asaparallel-form structure.
H(z)
H 1
(z)
x(n)
y(n)
H 2
(z)
FIGURE P6.7 Structure for Problem 6.14
P6.15 The digital filter structure shown in Figure P6.8 is a cascade of 2 parallel sections and
corresponds to a 10th-order IIR digital filter system function
H(z) =
1 − 2.2z−2 +1.6368z −4 − 0.48928z −6 + 5395456 × 10 −8 z −8 − 147456 × 10 −8 z −10
1 − 1.65z −2 +0.8778z −4 − 0.17281z −6 + 1057221 × 10 −8 z −8 − 893025 × 10 −10 z −10
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