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300 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS
2. Quantize the direct-form coefficients to 4 decimals (by rounding). Now plot the
log-magnitude and amplitude responses of the resulting filter. Use 2 rows and 1 column
of subplots.
3. Quantize the direct-form coefficients to 3 decimals (by rounding). Now plot the
log-magnitude and amplitude responses of the resulting filter. Use 2 rows and 1 column
of subplots.
4. Comment on the plots in parts 1, 2, and 3.
5. Based on the results of this problem, determine how many significant bits (and not
decimals) are needed in practice to represent FIR direct form realizations.
P6.37 The digital filter structure shown in Figure P6.9 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
4.0635
4.0635
−0.0793
−2.8255
−1.6
z −1
−0.0815
0.4
z −1
0.7747
−0.63
z −1
−0.03
z −1
x(n)
−0.5502
−0.2076
y(n)
−0.8
z −1
−0.2245
1.2
z −1
0.1319
−0.15
z −1
−0.35
z −1
−2.4609
−0.0304
−0.1
z −1
−0.9
z −1
FIGURE P6.9 Structure for Problem P6.37
1. Due to an error in labeling, two of the multiplier coefficients (rounded to 4 decimals) in
this structure have incorrect values. Locate these 2 multipliers and determine their
correct values.
2. By inspecting the pole locations of the system function H(z), you should realize that
this structure is sensitive to the coefficient quantization. Suggest, with justification, an
alternative structure that in your opinion is least sensitive to coefficient quantization.
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