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290 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS
P6.6 A causal linear time-invariant system is described by
4∑
5∑
y(n) = cos(0.1πk)x(n − k) − (0.8) k sin(0.1πk)y(n − k)
k=0
k=1
Determine and draw the block diagrams of the following structures. Compute the response
of the system to
x(n) =[1+2(−1) n ] , 0 ≤ n ≤ 50
in each case, using the following structures.
1. Normal direct form I
2. Transposed direct form II
3. Cascade form containing 2nd-order normal direct-form-II sections
4. Parallel form containing 2nd-order transposed direct-form-II sections
5. Lattice-ladder form
P6.7 An IIR filter is described by the following system function
( ) ( )
1+0z −1 + z −2
2 − z
−1
H(z) =2
+
+
1 − 0.8z −1 +0.64z −2 1 − 0.75z −1
( )
1+2z −1 + z −2
1+0.81z −2
Determine and draw the following structures.
1. Transposed direct form I
2. Normal direct form II
3. Cascade form containing transposed 2nd-order direct-form-II sections
4. Parallel form containing normal 2nd-order direct-form-II sections
5. Lattice-ladder form
P6.8 An IIR filter is described by the following system function
H(z) =
( ) ( )( )
−14.75 − 12.9z
−1 24.5+26.82z
−1 1+2z −1 + z −2
+
1 − 7 8 z−1 + 3 32 z−2 1 − z −1 + 1 2 z−2 1+0.81z −2
Determine and draw the following structures:
1. Normal direct form I
2. Normal direct form II
3. Cascade form containing transposed 2nd-order direct-form-II sections
4. Parallel form containing transposed 2nd-order direct-form-II sections
5. Lattice-ladder form
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