Hello

> Now: isn't the phase shift of this shifted signal, due to the
> physical effect of passing through some sort of filter (something
> like notch or BP)

No.

What we call a "filter circuit" is a circuit which has two
characteristics, which are both related to the center frequency, and
which change above and below the center frequency.
1.) The phase of the output signal in relation to the input signal
2.) The level of the out signal in relation to the input signal

In both cases this is not an abrupt change, but the change starts slowly
somewhere below the center frequency and ends somwhere above.
Both characteristics change at "the same time".

We know five kinds of filters: Lowpass, Bandpass, Notch, Highpass, and
Allpass

All of them have the phase behaviour in common.

But only four of them have the level behabviour in common:
* Lowpass: the output level above the center frequency is less than below
* Highpass: the output level above the center frequency is more than below
* Bandpass: the output level around the center frequency is more than
below and above
* Notch: the output level around the center frequency is less than below
and above

The allpass does not change the level, but still changes the phase.

You could use e.g. a Lowpass also for a phaser, but since there is also
this level-thing, the phaser effect would stop soon above the center
frequency: one ocatve above the center frequency there is nothing to mix
with the input signal anymore - it is filtered away already. Same for
all other types of filters. With exception of the allpass: The allpass
provides the wonderful phase shift, wothout spoiling the game by muting
the shifted frequencies.

A phaser works only with an allpass - nothing else. But the other way
around: a phaser never can be used as a filter.

Florian