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288 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS
Log-Mag Plot: 16-bits (1+0+15)
Log-Mag Plot: 8-bits (1+0+7)
0
True
16-bit
0
True
8-bit
−20
−20
Decibels
−40
Decibels
−40
−60
−60
−80
0 0.2 0.4 0.6 0.8 1
Digital Frequency in π Units
Imaginary Part
2
1
0
−1
PZ Plot: 16-bits (1+0+15)
16-bit zero
True zero
−80
0 0.2 0.4 0.6 0.8 1
Digital Frequency in π Units
PZ Plot: 8-bits (1+0+7)
2
8-bit zero
True zero
1
Imaginary Part
30 30
0
−1
−2
−2 −1 0 1 2
−2
−2 −1 0 1 2
Real Part
Real Part
FIGURE 6.35 Plots for the FIR filter in Example 6.29
When 16 bits are used, the resulting filter is virtually indistinguishable from
the original one. However, when 8 bits are used, the filter behavior is severely
distorted and the filter does not satisfy the design specifications. □
6.9 PROBLEMS
P6.1 Draw direct form I block diagram structures for each of the following LTI systems with
input node x(n) and output node y(n).
1. y(n) =x(n)+2x(n − 1)+3x(n − 2)
1
2. H(z) =
1 − 1.7z −1 +1.53z −2 − 0.648z −3
3. y(n) =1.7 y(n − 1) − 1.36 y(n − 2) + 0.576 y(n − 3) + x(n)
4. y(n) =1.6 y(n − 1)+0.64 y(n − 2) + x(n)+2x(n − 1) + x(n − 2)
1 − 3z −1 +3z −2 + z −3
5. H(z) =
1+0.2z −1 − 0.14z −2 +0.44z −3
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