____: Re: [PD] On arrays.

[Charles Henry]

> Yeah, I'm not getting much joy from that either :/

I'm still working on it....I've had some luck at improving it, but
I've managed to show there's some pesky effects from the windowed
short time fourier transform business.  The time I made it work for
some force control signals in the lab, I used the fourier transform of
the whole signal.

> I'm somewhat familiar with the principle I think, at least
> in practice as a "phase shifter" for removing sidebands
> with a quadrature mixer etc, but even though I understand
> Hilbert is fundamental there's a big hole in my maths in
> that subject, around about the point I fell asleep in
> engineering maths lectures.

We all fell asleep in engineering math lectures.  I just make it up as
I go along. (My brother looks at me sideways as I do this, all the
time)

> Can you give a description, in words rather than equations
> if possible please, how Hilbert arises and why its central
> to complex signals. Maybe with another example of why you
> would use the transform for a practical purpose.

I don't really have a text on this subject any more....so the details
are a little fuzzy where the hilbert transform comes from.....I can
tell you this, it's a funky integral equation with some kernel, that
has do to with the eigenvectors/eigenvalues of some linear
operator...but then, that's generally what all transforms are
about....I'll have to look it up again, just to make sure I have the
right idea.

for signal analysis, the whole idea is this: we can take any signal  ,
that has any number of frequencies, and transform it into a joint
amplitude/frequency modulation of a single frequency described by
amplitude and phase separately as functions of time.

In the lab, I was working on using this for analyzing force control
data, which showed a kind of damped resonance.  But it was a natural
signal so there was no clearly defined resonance.  Instead there were
several damped resonances of different frequencies.  When you plot the
hilbert tranform in the complex plane, you get a "phase plane" (is
that what it's called?) portrait of the signal.  There were decaying
slow frequencies of high amplitude, with some smaller higher
frequencies added in, which showed up as epicycles in the graph.
Ultimately, we scrapped the analysis, since it didn't seem like I
could make any significant conclusions.

> One thing that confuses me right now is how you can
> have a phase signal? Relative to what? That is why
> I said phase comparator, it kinda doesn;t make sense
> to me to have absolute phase, it must be relative to something.

To me, the phase is absolute.  It describes a relationship, at a
certain point in time, between the signal's value and it's rate of
change.

........
for improvement, maybe I should try doing it on the whole
signal....This sounds like a job for the script function.  I haven't
tried it yet, but this would be a good chance to learn.  I could make
a little script with octave that would take the hilbert transform of
the whole signal, and smoothly match the phase at the end of the file
to the beginning and return it....then the signal could be loaded as
an array, and could try looping it to see if it works.  sounds a
little ambitious at the moment.... 's getting late tonight

Have a good weekend!
Chuck