Exponental/Linear Modulation of Phase, + new circuit idea

[Sean Costello]

Haible Juergen wrote:

> 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 sure.  The delays used are single sample delays. However, I am fairly
certain that these allpass stages directly correspond to the analog allpass
stages. I replicated the Bernie Hutchins phase differencing network using
similar structures (which can now be found in the hilbert unit generator in
Csound), and have successfully constructed frequency shifters, barberpole
phasers, etc. using these structures, so I would presume that this behaves in a
similar fashion to a single-stage analog allpass filter. Once you have larger
delays (i.e. > 1 sample), it is a whole different ballgame, of course.
 
> 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 ?

Um...I have to admit that I don't have too much background in z-transforms and
such. I have been working on it, but needed to take the summer off for mental
health. :)  I used a Mike Beigel paper from the JAES to translate the Hutchins
pole values into useable allpass coefficients - I can't find it right now, but
the date is 1979 or so.

Sean Costello