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Quantization of Filter Coefficients 285
Log-Mag Plot: 16-bits (1+2+13)
Log-Mag Plot: 8-bits (1+2+13)
0
0
−20
−20
Decibels
−40
Decibels
−40
−60
True
16-bit
−60
True
8-bit
−80
0 0.2 0.4 0.6 0.8 1
Digital Frequency in π Units
PZ Plot: 16-bits (1+2+13)
1
−80
0 0.2 0.4 0.6 0.8 1
Digital Frequency in π Units
PZ Plot: 8-bits (1+2+5)
1
Imaginary Part
0.5
0
−0.5
16-bit zero
16-bit pole
True zero
True pole
Imaginary Part
0.5
0
−0.5
8-bit zero
8-bit pole
True zero
True pole
−1
−1
−1 −0.5 0 0.5 1
−1
Real Part
FIGURE 6.34 Plots for the IIR filter in Example 6.28
−0.5 0 0.5
Real Part
1
6.8.4 FIR FILTERS
A similar analysis can be done for FIR filters. Let the impulse response
of an FIR filter be h(n) with system response
Then,
H(z) =
∆H(z) =
M−1
∑
n=0
M−1
∑
n=0
h(n)z −n (6.78)
∆h(n)z −n (6.79)
where ∆H(z) isthe change due to change in the impulse response h(n).
Hence
∆H (e jω )=
M−1
∑
n=0
∆h(n)e −jωn or |∆H(e jω )|≤
M−1
∑
n=0
|∆h(n)| (6.80)
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