Infinite Impulse Response Filters - Digital Signal Processing and Applications with the C6713 and C6416 DSK - page 206

4. Three sets of coefficients associated with a fourth-, a sixth-, and an eighth-
order IIR filter were obtained using the DigiFilter package in Appendix E.
The center and sampling frequencies for each filter are 1250 and 10,000 Hz,
respectively. The filter design uses cascaded direct form II sections. Implement
an IIR filter in real time with each set of coefficients, using a sampling rate of
8 kHz (not 10 kHz). Determine the center frequencies of these filters and
compare the Butterworth filters in terms of selectivity (sharpness).

(a) Fourth-Order Elliptic
First Stage

Second Stage

a 0 0.078371 0.143733

a 1 - 0.148948 0.010366

a 2 0.078371 0.143733

b 1 - 1.549070 - 1.228110

b 2 0.968755 0.960698

(b) Sixth-Order Butterworth
First Stage Second Stage Third Stage

a 0 0.137056 0.122159 0.122254

a 1 0.0 0.0 0.0

a 2 - 0.137056 - 0.122159 - 0.122254

b 1 - 1.490630 - 1.152990 - 1.256790

b 2 0.886387 0.856946 0.755492

(c) Eighth-Order Butterworth
First Stage

Second Stage Third Stage Fourth Stage

a 0 0.123118 0.130612 0.127179 0.143859

a 1 0.0 0.0 0.0 0.0

a 2 - 0.123118 - 0.130612 - 0.127179 - 0.143859

b 1 - 1.18334 - 1.33850 - 1.15014 - 1.52176

b 2 0.754301 0.777976 0.884409 0.910547

REFERENCES

1. L. B. Jackson, Digital Filters and Signal Processing , Kluwer Academic, Norwell, MA,

1996.

2. L. B. Jackson, Roundoff noise analysis for fixed-point digital filters realized in cascade

or parallel form, IEEE Transactions on Audio and Electroacoustics , Vol. AU-18, June
1970, pp. 107-122.

3. L. B. Jackson, An analysis of limit cycles due to multiplicative rounding in recursive

digital filters, Proceedings of the 7th Allerton Conference on Circuit and System Theory ,
1969, pp. 69-78.