All pass filters?

[jhaible]

> >> Consider this: theory says you'll never be able to phase shift a
fourier
> >> frequency more than 180 deg in either direction.
> >
> >This I don't understand. Can you be more specific ?
> -i think what he means is that if you shift a given frequency is a
fourier
> series by more than |180| degrees (in respect to the other frequencies),
it
> looks just the same as having shifted it the other direction by a
> complementary amount.  i don't think this would be true in joint
> time-frequency analysis though.. 

Yes, steady state signals (with discrete harmonics) don't really exist in
real life.
If they would (i.e. last from eternity to eternity), you would indeed not
be able to decide a 361 degree shift from a 1 degree shift.
For all real life signals, larger than 360 degree phase shift is clearly
possible.
Just chain a handfull of all pass networks and feed them with a short
pulse.
A certain spectral component of this pulse will be shifted in phase by a
certain
amount (which can easily be larger than 360degree). This is equivalent to
being delayed by a certain time. I even prefer to look at the delay as 1st
order effect, and phase shift as a derived function. The filter is a medium

thru which the electric wave propagates, and this medium has a certain 
speed for the wave to go thru it. This speed is frequency dependent - I 
think for optical media and light waves it's called dispersion (?). In the
all 
pass filter this means that phase and delay are not a linear funtion over 
frequency.

So in real life, everything works fine. It's just the Fourier Transform of
strictly periodic signals which may lead to some confusion.

JH.