question for theorists: zeros & phase

[Magnus Danielson]

From: Martin Czech <martin.czech at intermetall.de>
Subject: RE: question for theorists: zeros & phase
Date: Mon, 27 Sep 1999 13:41:30 +0200 (MET DST)

> Ok, I accept that zeros on the imaginary axis pose no real problem,
> since that would mean no damping in the resonant circuit, and this would
> mean infinite measurement time in turn, even for a theoretical model.
> 
> But a zero at 0 is still allowed, one could argue that leakage prevents us
> from having such a zero, a theoretical model should have it, however. Now
> evalutaion from -inf to +inf would pose a problem there, but hey,
> there's our frequency shifter again, frequency has to turn from - to +
> , and in between frequency slows down, so that phase gets irrelevant.
> 
> And, 0 is never reached in a bode plot (for log reason).

You never actually have your zero(s) at origo in any real system. It is just
a very convenient approximation. Actually having anything dead beat on the
imaginary axis in a real system forms a problem.

There are these devices (for which people love to discuss here) which have
spread a number of poles along the imaginary axis. But since it is a problem
to keep things dead beat on the imaginary axis these devices depends on
various nonlinear systems to keep the poles swing in some pattern around
a centrum point on the imaginary axis with the net effect of being there.
These devices is called oscillators and their use should be known to the
audience.

Also, you can temporary move these points around, when you do it along the
imaginary axis we call it frequency modulation and when we do it along the
real axis we call it amplitude modulation (well, this is roughly the truth).

Then people stick in more poles and zeros and move them separately, this we
call filters, eq's, phasers, reverbs etc.

> In dicrete systems it turns out that the problem is not so sharp, since
> the sign of phase change is allways defined, because the imag axis was
> sqeezed into a circle.
> 
> I think I understand better now.

Ah, how nice ;)

> Thank you for the information.

Anytime, you know that!

Cheers,
Magnus