revisiting that Bode Phaser

[jh.]

I've posted a short comment about the working principle of the
4.399.326 patent recently.
More thinking since then - it's even easier than I thought.

Forget about that frequency shifter part. Sure, the structure is there,
and you *need* it, but it's quite misleading to look at it in its frequency
shifting function. Let's look at it from a different point of view, as a
"phase interpolator".

I try to explain that.

Take an ordinary phaser. Mix the output of the all pass filtered signal
(AP signal) with the input signal. You get a certain pattern of notches (1).

Now mix that AP signal with the inverted (180 degree phased) input
signal, and you get a different, somewhat complementary pattern of
notches (2).

That's the ordinary phasers, so far.

Wouldn't it be fine to have everything in between these cases (1) and (2) ?
Crossfading between the noninverted and inverted signal does not help,
because you only get 0 deg and 180 deg signals with decreasing amplitude.
What you want instead is a device to continously change the phase from
0 deg to 180 deg (and further on to 360 deg).

How can this be done ? If you have a 0 deg signal and a 90 deg signal,
you can get any other phase shift by linear combination, like
sin (x + phi) = A sin(x) + B cos(x).
That's exactly what the apparatus of patent 4.399.326 does. The quadrature
LFO (or the joystick, for that matter) picks a cyclically changing  (or
arbitrary,
in case of joystick) mix of the normal and the quadrature input signal.

No frequency shifting needed. Sure, if you're moving the joystick, or when
that quadrature LFO is running, there *is* also some frequency shifting
(just as there is some pitch shifting in flanging), but this is merely a
side
effect. (And if you would run that LFO (or joystick) very fast, at some
point
the FS effect would become prominent and possibly mask the phasing effect.)
But the important thing is that the *phasing* effect is not based on the
frequency
shifting. The phasing is there, even with your sloooowwwwest movement
of the joystick.

I'm sure the similar topology of a FS and that phasing apparatus is more
than
"coincidence" (there is nothing such as coincidence in maths), but to
explain
that phasing effect there is no need for a concept of frequency
modulation/shift
at all.
It's pure slow, LFO-rate, modulation of the phase which causes the phasing
effect in patent 4.399.326. I even prefer the word "phase interpolation",
because
it reflects the method how the effect is created: A hilbert transformator,
and
two "voltage controlled reversible attenuators" to mix the desired phase
from
two orthogonal basic signals.

I hope you found this interesting - comments welcome !
(Of course it's nothing really new; I just wanted to share that "click" of
finally understandig it.)

JH.