[PD] phase locked loop

[Charles Z Henry]

On Mon, Mar 13, 2023 at 8:32 AM Charles Z Henry <czhenry at gmail.com> wrote:
>
> On Mon, Mar 13, 2023 at 7:41 AM Simon Iten <itensimon at gmail.com> wrote:

> > i do not currently grasp the math in the fexpr~ objects, but will try to get into it…
>
> It's a simple kind of dynamical system.  It responds based on its
> inputs but also its internal state when receiving inputs.  That's why
> [fexpr~] works well for this.  You can add additional expressions and
> reference them from each other.  There can be internal hidden state
> variables, etc....

Right now, I just left the outlets all hanging out of synch_osc~ for
debugging.  Connect up some plots (maybe longer block sizes would be
better) to see what's in the

I'd say it's actually the *simplest* kind of dynamical system for
phase locking (and a very artificial one).  It's just a discretized,
noise-less little phasor. e.g.

[fexpr~ modf($y1+1.0/44100)]
is just a phasor that counts from 0 up to 1 over 44100 samples

So, if I want, I'll change that to use [samplerate~] and pass in
1/samplerate as a float $f2
[fexpr~ modf($y1+$f2)]

Now, add frequency in $y2, and multiply
[fexpr~ modf($y1+$y2*$f2);
80]
It's a 80 Hz phasor.

Next, I extend the phase that's stored in $y1 so it accumulates over
time between impulses from $x1 in $y3
[fexpr~ modf($y1+$y2*$f2);
80;
if($x1==1, $y1, $y3+$y2*$f2])

So, now I have phase and freq as functions of time, and I'll add in
some updates to the terms and put them in $y4, $y5 so that the updates
get added in when receiving an impulse from $x1
[fexpr~ modf($y1+$y2*$f2+$y4*$x1);
80 + $y5*$x1;
if($x1==1, $y1, $y3+$y2*$f2]);
($y4) phase update function of $y3;
($y5) freq update function of $y3 ]

With some re-ordering of things and adding in parameters and scaling
coefficients with $f inlets, that's basically what's in synch_osc~
right now

The choice of the phase and frequency update functions is what causes
the synchronization.

For anyone who's interested in some light reading (LOL), I noticed
Izhikevich has put "Dynamical Systems in Neuroscience" (~500 pgs) in
pdf at https://www.izhikevich.org/publications/
Chapter 10 is on synchronization and it has a section on
phase-locking.  It took me over a year to read this, much of the math
eludes me also

I want to make a version that's good for your hexaphonic pickup, you
know that just works well as a sensor and has clean output.
synch_osc~.pd has problems with low frequencies and I know where that
comes from
I think it has to be 6 PLL's, each tuned to the range of each string.
Can you tell me what the range is on your instrument?

Best,
Chuck