[music-dsp] crossover filters for compressor

[Didier Dambrin]

Filters in RBJ's cookbook are butterworth when not resonant? I didn't know 
that.
Right when I thought I started to understand IIR filters...


I'll try that, thanks




> Hello Didier,
>
> Butterworth filters should have a DC gain of 0 dB. The page you have 
> linked
> normalizes the output to unity gain at DC, so you don't need to multiply
> coeffs.
>
> You could use RBJ cookbook lowpass/highpass filters with a Q value of sqrt
> (2)/2 = 0.7071 to calculate biquad coeffs for LP/HP Butterworth filters. 
> You
> cascade two of these serially, and you get 24 dB/oct L-R crossover 
> filters,
> which sum flat and have unity gain.
>
> Best,
> Peter
>
>
> On Mon, 19 Mar 2007 17:45:44 +0100, Didier Dambrin wrote
>> A question about butterworth (trying to implement the 24dB one):
>> I've found several implementations, but none seemed to deal with the
>> gain introduced.
>>
>> If I want the filtered bands to sum up as the original signal, I
>> have to multiply my feedforward coefficients by the DC gain as
>> computed here, right?
>>
>> http://www-users.cs.york.ac.uk/~fisher/mkfilter/trad.html
>>
>> > Hello Didier,
>> >
>> > Flat summing IIR crossover filters:
>> >
>> > - 6 dB/oct Butterworth: Use 1 pole lowpass, subtract lowpass out from
>> > input to get highpass out.
>> >
>> > - 12 dB/oct Linkwitz-Riley: Process input using 2 pole lowpass & 
>> > highpass
>> > filter at the same frequency with q = 0.5, invert polarity of one band 
>> > to
>> > make the outputs in phase.
>> >
>> > - 18 dB/oct Butterworth: Use 3 pole lowpass/highpass Butterworth 
>> > filters
>> > (q = 0.7071). You can do that by serially cascading a 2 pole filter 
>> > with
> q
>> > = 1.0 and a one pole filter.
>> >
>> > - 24 dB/oct Linkwitz-Riley: Use 2 pole lowpass/highpass Butterworth
>> > filters (q=0.7071), process both LP and HP channel *twice* using two
>> > filters (so you get a 24 dB/oct slope for both LP and HP). Don't need 
>> > to
>> > invert polarity here.
>> >
>> > These filters are all commonly used in loudspeaker design, and they all
>> > sum to perfectly flat. They work well with compressors (and other
>> > multiband applications as well).
>> >
>> > Versions exist with steeper slopes too, but transient response of them 
>> > is
>> > not that good, so they may be of less use. Of course you can add more
>> > filters to create more bands:
>> >
>> > input -> lp1 --------> low band
>> > input -> hp1 -> lp2 -> mid band
>> > input -> hp2 --------> high band
>> >
>> > etc.
>> >
>> > Best,
>> > Peter
>> >
>> >
>> > Didier Dambrin wrote:
>> >> I was thinking of what could work as a good crossover filter for a 3-
> band
>> >> multiband compressor, without using FIR's.
>> >>
>> >> I can imagine:
>> >>
>> >>
>> >> -a simple lowpass & highpass (or 2 lowpass), subtracted from the
> original
>> >> signal to give the third band. But due to phasing problems, this will
>> >> work only with simple 6dB IIRs, right?
>> >>
>> >>
>> >> -a higher-order low & highpass, and live with the fact that the mid 
>> >> band
>> >> would be more the residual than the mid band.
>> >> I'm only worried that each band won't have the same compression
> settings,
>> >> so they should be separated enough. But maybe it's not important.
>> >>
>> >>
>> >> -a low & highpass, but involving 2 allpass to correct the phase 
>> >> problem
>> >> so that the residual will really be the mid. I have no idea how to
>> >> compute that allpass, and if it's even doable, though.
>> >>
>> >>
>> >> -a low, band & highpass, living with the fact they won't sum up like 
>> >> the
>> >> original signal (or are there IIR's designed for this?)
>> >>
>> >>
>> >> -using minimum-phase IIR's? Are there IIR's really better than others
> for
>> >> this kind of stuff? I don't know much about this either.
>> >>
>> >>
>> >> I was wondering if one of those methods was more common than the 
>> >> others.
>> >>
>> >> thanks
>> >> -- 
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