Exponental/Linear Modulation of Phase, + new circuit idea
Haible Juergen
Juergen.Haible at nbgm.siemens.de
Thu Aug 5 16:23:42 CEST 1999
>This refers to the gain coefficient of the feedforward/feedback
amount
>in the difference equation used in Csound. The allpass equation
looks
>like this:
>
>y(n) = g*x(n) + x(n-1) - g*y(n-1)
>
>where x(n) is the input, x(n-1) is the previous input, y(n) is the
>output, y(n-1) is the previous output, and g is the gain
coefficient. g
>MUST be between -1 and 1; otherwise, the whole thing "blows up"
almost
>instantly, with the amplitude quickly exceeding the range of the
>floating point representation. The "fold over" was originally used
as a
>way of dealing with this problem - it was somewhat accidental that
I
>discovered it sounded good.
Ah I see (or at least hope I do).
This would be quite different from an analogue all pass stage, wouldn't it ?
You only have one unity delay per stage. Is that one sample period, or
a multiple of sample periods ? I can roughly see how you can change the
behaviour of the circuit by changing g, but while still being an all pass
function, I asume the phase frequency response would be quite different
from the analoge solution (if you don't change the unity delay as well).
I'm not more than guessing / asuming right now. Have you written down
the frequency response of the filter (z transform (exp(jwT) ) resolved
to f(jw) in the base band), to make comparison with the analoge stage
easier ?
Or a phase plot ?
JH.
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