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Round-off Effects in IIR Digital Filters 575
Distribution of Output Error
0.0313
0.0234
0.0156
0.0078
SAMPLE SIZE N = 100000
RADIAL r = 0.9
SNR(THEORY) = 25.2243
SNR(LOWER) = 20.8906
ROUNDED TO B = 6 BITS
ANGLE THETA = 60 DEG
SNR(COMPUTED) = 25.1065
SNR(UPPER) = 26.4697
0
−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5
Normalized Error
FIGURE 10.23 Multiplication quantization effects in the 1st-order IIR filter in
Example 10.12, B =6bits
second-order filter section is filtered by the succeeding sections. To minimize
the total noise power at the output of the high-order filter, a
reasonable strategy is to place the sections in the order of decreasing maximum
frequency gain. In this case the noise power generated in the early
Distribution of Output Error
0.0313
0.0234
0.0156
0.0078
SAMPLE SIZE N = 100000
RADIAL r = 0.9
SNR(THEORY) = 61.3443
SNR(LOWER) = 57.0106
ROUNDED TO B = 12 BITS
ANGLE THETA = 60 DEG
SNR(COMPUTED) = 61.3968
SNR(UPPER) = 62.5897
0
−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5
Normalized Error
FIGURE 10.24 Multiplication quantization effects in the 1st-order IIR filter in
Example 10.12, B =12bits
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