I could not find any info on them. I made two variants:

1) a continuous interpolation between

*n*th-order Butterworth filters

*G(w) = (1 + w^(2*n))^(-1/2))*. It starts at 6dB/oct and preserves the constant response of -3 dB at the cutoff frequency. The interpolation works by simply moving poles and zeros like this (z-plane):

2) an approximation of the gain function

*G(w) = 1/(1 + w^n)*with Padé rational functions. It is simple enough as well and allows for gradual slope change starting from 0, but it requires numerically finding roots of some 12th-degree polynomials for every new slope value, in order to split the filter into biquad sections.

I'm curious if there are any other methods or common practices for implementing such filters.