Estimating phase of Noisy Sinusoidal Signal

On Feb 6, 1:36&#4294967295;am, "steveu" <ste...@coppice.org> wrote:
> >On Feb 6, 12:24=A0am, spop...@speedymail.org (Steve Pope) wrote:
> >> robert bristow-johnson =A0<r...@audioimagination.com> wrote:
>
> >> >do you know anything about the range of phase shift between any pair?
> >> >if it is between 0 and pi, then you won't need to H.T. the reference
> >> >sinusoid to generate a quadrature reference sine. =A0if you have no
> idea
> >> >what the phase relationship is, you need both the I and the Q.
>
> >> I'm not seeing why you would ever need to Hilbert Transform
> >> any signal for this problem.
>
> >because of two reasons. &#4294967295;(if either was not the case, he wouldn't have
> >to.)
>
> >first, the OP is not generating the reference sinusoid. &#4294967295;if he was, he
> >could just as well generate a synced sine that was 90 degrees outa
> >phase (like in the other current thread about this same topic).
>
> >second, because of quadrant ambiguity (if he already knows he's in
> >quadrants I or II, it's no problem, he does an arccos() instead of an
> >arctan()), he needs to correlate the sinusoid of unknown phase against
> >both the reference sinusoid and the quadrature component of the
> >reference sinusoid. &#4294967295;if you can settle the quadrant ambiguity more
> >easily (say, by looking at zero crossings, but remember this is
> >noisy), then fine - no need for HT.
>
> >anyway, that's my spin on it.
>
> Under noisy conditions, the arc cos approach has an accuracy that varies
> hugely with the angle. You mentioned the noise issue in relation to
> identifying zero crossings, but the effect of noise at particular angles is
> a bigger problem. The arc tan approach offers comparable accuracy all the
> way from 0 to 360 degrees.

most certainly true.

r b-j

steveu wrote:
(snip)

> Under noisy conditions, the arc cos approach has an accuracy that varies
> hugely with the angle. You mentioned the noise issue in relation to
> identifying zero crossings, but the effect of noise at particular angles is
> a bigger problem. The arc tan approach offers comparable accuracy all the
> way from 0 to 360 degrees.

Can someone remind me if there is an analog arctangent amplifier?

I seem to remember one, but I don't remember where and I didn't
find it with Google.

That is, two inputs X and Y, with an output voltage proportional
to atan2(y,x).

-- glen

On Feb 6, 6:59&#4294967295;pm, Glen Herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
> steveu wrote:
>
> (snip)
>
> > Under noisy conditions, the arc cos approach has an accuracy that varies
> > hugely with the angle. You mentioned the noise issue in relation to
> > identifying zero crossings, but the effect of noise at particular angles is
> > a bigger problem. The arc tan approach offers comparable accuracy all the
> > way from 0 to 360 degrees.
>
> Can someone remind me if there is an analog arctangent amplifier?
>
> I seem to remember one, but I don't remember where and I didn't
> find it with Google.
>
> That is, two inputs X and Y, with an output voltage proportional
> to atan2(y,x).

i haven't seen that, but back in the '70s, right when digital
simulation and control of systems was essentially replacing analog, we
had a big analog computer (i can't remember the manufacturer) donated
to the EE dept. where i was an undergrad.  they had all sorts of
functions, adders/subtracters, gain blocks, multipliers, exp and log
amps, and  i thought that it had a simple Vy*arctan(v/Vx) where Vx and
Vy were known fixed voltage scalers.  i thought that i looked at some
three-ring binder documentation, and this arctan() was done simply
with diodes or transistors wired similarly to implement soft break
points.  i can't remember how many, but i remember that there were
1/2% resistors, so this couldn't have been all that good unless they
somehow tweaked it during construction.  each function module was
encased in some kinda plastic or resin-filled block with real solid
post terminals coming out of it.  i've seen some similarly encased
high-quality difference amps called "instrumentation amps" (i might
even have some in an old electronics junk box).

our control theory prof used this with a chart recorder to demonstrate
some systems with time constants around a second (so you could see the
ringing on the chart recorder).

r b-j

robert bristow-johnson wrote:
(snip, I wrote)

>>Can someone remind me if there is an analog arctangent amplifier?

> i haven't seen that, but back in the '70s, right when digital
> simulation and control of systems was essentially replacing analog, we
> had a big analog computer (i can't remember the manufacturer) donated
> to the EE dept. where i was an undergrad.  they had all sorts of
> functions, adders/subtracters, gain blocks, multipliers, exp and log
> amps, and  

I did see log, exp, and sqrt amplifiers.  There are also dividers,
though I am not so sure about four quadrant dividers.
(One way to divide is with two log amplifiers, subtract,
and then exp.)  This being the DSP group, one should go through
an A/D converter, compute the atan2 numerically, then D/A back.
That should fit in a nice small box.

-- glen

On Feb 6, 11:59&#4294967295;pm, Glen Herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
...
> I did see log, exp, and sqrt amplifiers. &#4294967295;There are also dividers,
> though I am not so sure about four quadrant dividers.

i am not saying that these big-board analog computers were made from
ADI parts (from the 60s or early 70s), but i know that ADI had
circuits to do all of that (except maybe arctan).

> (One way to divide is with two log amplifiers, subtract,
> and then exp.) &#4294967295;This being the DSP group, one should go through
> an A/D converter, compute the atan2 numerically, then D/A back.
> That should fit in a nice small box.

actually, what is better if *all* of it (the various functional
blocks) live virtually inside the box.  that would just be a modular
design of digital simulators of the different functions.  in the 90s i
worked at Eventide and we made the first (as far as i know) modular
multi-effects box where blocks could be plopped down and connected on
the screen and inside the box that composite algorithm lived (and you
could plug your electric guitar into it).

but they still do it analogly with pedal boards.  maybe there your
atan2 box would go.

r b-j