[sdiy] Analysis filter bank help

[Richie Burnett]

> Chebyshev filters are known for steeper rolloff.  Indeed, an 8th-order
> Chebyshev filter has the same rolloff as a 19th-order Butterworth filter. 
> A
> Chebyshev II filter has a less steep rolloff, but no ripple in the 
> passband.
> An elliptic filter would have an even steeper rolloff than a Chebyshev
> filter.
>
> I'm not sure you're going to do much better.

I totally agree, David.  My problem is how to design these Chebyshev filters 
to join on to the ends of the bank of bandpass filters without their outputs 
messing up the overall combined response.

Jurgen Haible was obviously onto something by choosing Chebyshev filters for 
his bottom and top bands.  And, as you can see from the combined response 
graph on his web page these LP and HP filters don't trash the overall 
response too much when their outputs are mixed in.  There's a bit more 
ripple at the LF and HF ends but not too bad.

I realise that what trashes the combined response is constructive and 
destructive interference between the outputs of the various filters when 
they're mixed.  That much I understand.  Using Linkwitz-Riley filters for 
the bandpasses makes sure that adjacent band-edges meet at -6dB and 
in-phase, so summing to unity as they overlap.  I just don't know how to 
work the same magic with the Chebyshev lowpass at the bottom and the 
Chebyshev highpass filter at the top!  I think it has something to do with 
keeping the Chebyshev filter's output in-phase with the output from the band 
that it is adjacent to for the region where both filters output significent 
energy.  If the phase relationship between the Cheby's output and the 
bandpass's output varies drastically where they overlap there's gonna be 
lots of nasty peaks and dips in the combined response.

-Richie,