Tables of novel Allpole Filters
Below tables of novel allpole filters are given which fulfill the specifications exactly.
Clicking on the entries leads to a window which contains the poles of filters having degrees n, where nT ≤ n ≤ nB-1 which fullfill the specifications exactly.
Tables
ωs=2.0
| αp \ αs | 20 dB | 25 dB | 30 dB | 35 dB | 40 dB | 45 dB | 50 dB | 55 dB | 60 dB | 65 dB |
| 0.1 dB |
[0.1,20,2.0] |
[0.1,25,2.0] |
[0.1,30,2.0] |
[0.1,35,2.0] |
[0.1,40,2.0] |
[0.1,45,2.0] |
[0.1,50,2.0] |
[0.1,55,2.0] |
[0.1,60,2.0] |
[0.1,65,2.0] |
| 0.5 dB |
[0.5,20,2.0] |
[0.5,25,2.0] |
[0.5,30,2.0] |
[0.5,35,2.0] |
[0.5,40,2.0] |
[0.5,45,2.0] |
[0.5,50,2.0] |
[0.5,55,2.0] |
[0.5,60,2.0] |
[0.5,65,2.0] |
1.0 dB |
[1.0,20,2.0] |
[1.0,25,2.0] |
[1.0,30,2.0] |
[1.0,35,2.0] |
[1.0,40,2.0] |
[1.0,45,2.0] |
[1.0,50,2.0] |
[1.0,55,2.0] |
[1.0,60,2.0] |
[1.0,65,2.0] |
| 3.0 dB |
[3.0,20,2.0] |
[3.0,25,2.0] |
[3.0,30,2.0] |
[3.0,35,2.0] |
[3.0,40,2.0] |
[3.0,45,2.0] |
[3.0,50,2.0] |
[3.0,55,2.0] |
[3.0,60,2.0] |
[3.0,65,2.0] |
Example
Assume you need a filter having the following specification:
A passband attenuation of 0.1 dB and a stopband attenuation of 30 dB beginning at ωs=2.
If you select a Tschebyscheff filter, you need a degree of nT=5 to fulfill the specification.
If you select a Butterworth filter, the degree is nB=8.
If the passband requirement is fulfilled exactly, the Tschebyscheff filter has a stopband attenuation of 34.85 dB.
If the passband requirement is fulfilled exactly, the Butterworth filter has a stopband attenuation of 31.84 dB.
If you select the novel filter designs, you get filters of degrees n=5, 6, and 7 which fulfill the specification exactly.
For n=5 the passband ripples of the new design are much smaller than the ripples of the Tschebyscheff filter with same degree: see here.
For n=6 the passband ripples are hardly noticable: see here.
For n=7 the passband ripples of the new design are not noticable anymore and the design has one degree less than the Butterworth design: see here.
For further details see my paper K. Huber, 'All-Pole Filters Matched to Specifications', Journal of the Audio Engineering Society,Vol.61, No.12, pp.1022-1025, December 2013 .
The poles of the novel designs for degrees n=5,6,7 are contained in the above tables (row 0.1dB, column 30 dB).
For custom designs send an email to filterdesign@klaus-huber.net containing αp, αs, and ωs.