[music-dsp] crossover filters for compressor

[James Chandler Jr]

Hi Didier

Any second-order filter with a Q = 1 / sqrt(2), will be Butterworth, if it is 
designed correctly. Doesn't matter if it is passive analog, active analog, or 
digital, as long as it has that exact Q value. Maybe some designs would need 
gain correction to get the passband gain == 1.0. I think the RBJ filters are 
properly gain-normalized out-of-the-box.

When you put two of the second-order butterworths in series, you get a Q of 0.5, 
and the amplitude is -6 dB down at Fc.

The hipass phase is advanced by pi at Fc, and the lopass phase is retarded by pi 
at Fc, so they are 'in phase' at the crossover point. Actually, the hipass and 
lopass are 2pi out of phase over the entire frequency range, but that mostly 
works out the same thing as 'allways in phase with each other'.

Since at Fc the hipass and lopass are both -6dB down and 'in phase', it sums 
flat when you add em back together.

JCJR