[sdiy] multimode matrix filter question

[David G. Dixon]

Hey Team,

This is a fairly arcane question with a big boring windup, but, oh well,
here goes:

I'm designing a multimode matrix filter interface for my 2164 4P LPF, and
I'm in a little bit of a quandary about what to do about overall gain for
some of the derived filter modes.  For example, a +12dB/-12dB BP filter mode
has the following general transfer function:

   s^2
---------
(s + 1)^4

If the following convention is used to describe the gain factors for the
cascaded 4P LPF input and four outputs:

A = gain factor of the LPF input
B = gain factor of the (inverted) 6dB LPF output
C = gain factor of the 12dB LPF output
D = gain factor of the (inverted) 18dB LPF output
E = gain factor of the 24dB LPF output

then this BP response can be obtained via the following gain factors:

{A,B,C,D,E} = {0,0,1,2,1}

However, at zero resonance, this gives -12dB attenuation at the centre
frequency.  To obtain 0dB attenuation (i.e., unity gain) at the centre
frequency requires the following transfer function:

  4 s^2
---------
(s + 1)^4

which requires the following gain factors:

{A,B,C,D,E} = {0,0,4,8,4}

So, finally, here is my question.  Do you think it would be better to design
all of the various filter responses so that the maximum amplitude at zero
resonance is roughly 0dB, or rather to do whatever is dictated by the
general transfer functions?  What would you want from such a filter?  Note
that setting the overall gain of each response involves altering the value
of a single (feedback) resistor, so it's not a big deal to change it after
the fact.