[music-dsp] Prewarping formula for bandpass transformation?

[Brent Lehman]

> From: Martin Eisenberg <martin.eisenberg at udo.edu>
>
> Brent Lehman wrote:
> 
> > If the coefficients of a filter are c[k] and the response is
> > C(w), the response of 2*cos(kf)*c[k] will be something like
> > C(w+f)+C(w-f).  In the case of a lowpass, where you had one
> > peak at w=0, now you have peaks at w=-f and w=+f.
> 
> This applies to nonrecursive filters.

Oh, right.  I guess in the general case if 

SUM{cos(kf) b[k] y[n-k]} = SUM{cos(kf) a[k] x[n-k]}

you get the response

H(w) = [X(w+f) + X(w-f)] / [Y(w+f) + Y(w-f)]

right?

You could do something like

SUM{exp(ikf) b[k] y1[n-k]} = SUM{exp(ikf) a[k] x[n-k]}
y[n] = 2 Re{y1[k]}

but even then, now that I think about it, phase cancellation can screw this up.  Adding responses together like this can scramble the locations of zeros -- poles less so, I suppose.

So never mind.