question for theorists: zeros & phase

[Haible Juergen]

	>Hello theorists, I'm just putting together a little program to
	>compute phase and magnitude for continuous and discrete filters.
This
	>is not difficult, all is written in the books.  We can read there
	>phase=arctan{Im/Re}. Oh, really? This is lovely academia. What
happens if
	>the pole/zero is very very close to the imaginary axis (unit
circle)? Ther
	>phase vector suddenly turns allmost 180 DEG. Due to the ambiguity
of the
	>arctan you get artefacts, phase jumps, oh well, one can eliminate
that,
	>but it causes some headache.
	>
	>But one real phase jump remains: a zero on the imaginary axis, or
on
	>the unit circle.  In both cases the phase vector comes closer and
closer
	>to the zero, and then it jumps 180 DEG to the other side
(especially in
	>the continuous case).
	>
	>It is clear to me that just at the zero the vector vanishes, so the
	>phase does have no meaning there. Especially in the case of
continuous
	>filters the question remains, if the phase jumps by +180 or -180
DEG at
	>the zero. Both would lead to the same phase vector, but different
bode
	>plots. To make things more confusing, zeros on the left side
(inside
	>unit circle) have a positive rotation whereas zeros on the right
side
	>(outside circle) have a negative rotation. So one can not argument
by
	>slowly approaching the imaginary axis (circle).
	>
	>Since I expect a nonambigous bode plot for a stable pole/zero
	>configuration there must be another restriction, I guess impulse
	>response ?
	>
	>??
	>
	>m.c.

Let me put it this way: The whole concept of "phase" makes assumptions
that idealize reality. In many cases it's close enough to real life, and
that's where
it works and does a great job for calculation. 
But the more you leave real conditions, the more you get strange results.
Does phase "jump" ? Not in real life of filter technology. (And let's not
talk
quantum physics here (;->)) Phase can *rapidly* change polarity at the
maximum
of a high Q filter. Now the theorist comes and says it "jumps" in a filter
with "infinite Q". And maybe he forgets for a moment that "phase" only makes
sense on a periodic signal. But when a signal is periodic, it doesn't change
it's form in infinite time, i.e. there is no way to approach the resonant
peak
of a filter from one side and cross it, with such a signal. Unless you
approach
it with "infinite slow change of frequency", of course. But then you'd spend
an infinite amount of time, and a phase difference of 360 degrees might
be swallowed by that.

JH.