# Re: Uncertainty principle debate

```Hi, everybody,

This question was asked on comp.dsp user group last year.
I hate to waste a good answer.
So here it is, and believe it or not,
it directly applies to the subject of your discussion.

__Subject__: Can I Extract Fundamental from Partial Sine Wave?
__Date__: Sun, 16 Nov 2003 03:55:36 -0600

> I have some experimental data for In-phase and quadrature signals.
> Sometimes the data covers only half or less, of a full cycle.
There are
> usually about 100 - 140 equally spaced (in time) points, but a few
> points are often missing.
>
> What technique can I use to calculate the fundamental frequency of
the
> sine wave?   I would like to write a program, or use a spread sheet,
> which ever is appropriate, or use an existing procedure.
>
> Any help would be appreciated.
>
> --
> Regards
>
>         Clive    G3CWV
>
>         Hitchin, North Hertfordshire, UK.

Jerry Avins <[EMAIL PROTECTED]> wrote in message news:<[EMAIL
PROTECTED]>...
>
> > Clive,
> >
> > What you are trying to find are the A, w and fi parameters for the
> > equation:
> >  A*exp(jwt + fi)
> > which makes the best fit with your data. You can do it with
> > autoregression.
> >
> >
> > DSP and Mixed Signal Design Consultant
> >
> > http://www.abvolt.com
>
> It's not quite that simple. As given, the waveform can have
harmonics.
>
> Jerry

If your signal is a pure sine wave (maybe noisy), then try to best-fit
the

If your signal is periodic but has an unknown harmonic structure, then
you
need more than one period to determine the fundamental period of a
signal.

All of the conventional methods (correlation, spectrum, cepstrum-based
etc.) used
for detecting fundamental period of a signal require at least 2
complete periods to be included in the analysis window (Well, you can
try to reduce your window size with
cross-correlation, but this is not a way to go).

The only method which can reliably get you the period (or its inverse
– fundamental frequency) of a periodic signal using analysis window
slightly longer than one complete period (at least for clean periodic
signals) is the method based on signal embedding in multi-dimensional
state space followed by a nearest-neighbor search. It was first
presented at ICASSP last year.

Go to http://www.soundmathtech.com/pitch