Hardware and Software for Digital Signal Processors - Digital Signal Processing: Fundamentals and Applications - page 446

0 : 0201 0 : 0402 z 2 þ 0 : 0201 z 4

HðzÞ¼

1 2 : 1192 z 1 þ 2 : 6952 z 2 1 : 6924 z 3 þ 0 : 6414 z 4

wðnÞ¼xðnÞþ 2 : 1192 wðn 1 Þ 2 : 6952 wðn 2 Þþ 1 : 6924 wðn 3 Þ 0 : 6414 wðn 4 Þ

yðnÞ¼ 0 : 0201 wðnÞ 0 : 0402 wðn 2 Þþ 0 : 0201 wðn 4 Þ

Using MATLAB to calculate the scale factor S , it follows that

» h ¼ impz([1],[1 2.1192 2.6952 1.6924 0.6414]);

» sf ¼ sum(abs(h))

28.2196
Hence we choose S ¼ 32. To scale the filter coefficients in the Q-15 format, we use the factors A ¼ 4
and B ¼ 1. Then the developed DSP equations are
x s ðnÞ¼xðnÞ= 32

sf ¼

w s ðnÞ¼ 0 : 25 x s ðnÞþ 0 : 5298 w s ðn 1 Þ 0 : 6738 w s ðn 2 Þþ 0 : 4231 w s ðn 3 Þ 0 : 16035 w s ðn 4 Þ

wðnÞ¼ 4 w s ðnÞ

y s ðnÞ¼ 0 : 0201 wðnÞ 0 : 0402 wðn 2 Þþ 0 : 0201 wðn 4 Þ

yðnÞ¼ 32 y s ðnÞ

Using the method described in Section 9.5, we can convert filter coefficients into the Q-15 format; each
coefficient is listed in Table 9.4 .

Table 9.4 Filter Coefficients in Q-15 Format
IIR Filter Filter Coefficients Q-15 Format (Hex)

0.5298 0 43D0

a 1

0.6738 0 A9C1

a 2

0.4230 0 3628

a 3

0.16035 0 EB7A

a 4

0.0201 0 0293

b 0

0.0000 0 0000

b 1

0.0402 0 FADB

b 2

0.0000 0 000

b 3

0.0201 0 0293

b 4