TABLE OF CONTENTS When an ideal low-pass filter characteristic is approximated by an all-pole function of the form
the various demonimator polynomials have the following coefficients.
Butterworth filters Table B-1 gives the polynomials for n up to 10 and a 0 normalized to unity. For n ? 4, see Table 1-1.
| n | Butterworth Polynomials |
|---|---|
| 5 | s 5 + 3.2361 s 4 + 5.2361 s 3 + 5.2361 s 2 + 3.2361 s + 1 ( s + 1.0000)[( s + 0.3090) 2 + 0.9511 2][( s + 0.8090) 2 + 0.5878 2] |
| 6 | s6 + 3.8637 s 5 + 7.4641 s 4 + 9.1416 s 3 + 7.4641 s 2 + 3.8637 s + 1 [( s + 0.2588) 2 + 0.9659 2][( s + 0.7071) 2 + 0.7071 2][( s + 0.9659)2 + 0.25882] |
| 7 | s 7 + 4.4940 s 6 + 10.0978 s 5 + 14.5918 s 4 + 14.5918 s 3 + 10.0978 s 2 + 4.4940 s + 1 ( s + 1.0000)[( s + 0.2225) 2 + 0.97492][( s + 0.6235) 2 + 0.78182] [( s + 0.9010)2 + 0.4339 2] |
| 8 | s 8 + 5.1258 s 7 + 13.1317 s 6 + 21.8462 s 5 |
