[vsnet-chat 242] Re: PDM troubles

[Taichi Kato <tkato@kusastro.kyoto-u.ac.jp>]

Fraser Farrell wrote:

> I recently read a paper by Fernie (PASP 101, 225-228 (Feb 1989)) which
> describes a simple algorithm for determining period uncertainty.
> 
> Fernie's method does a least-squares fit of a parabola to the "valley"
> (PDM plot) or "peak" (Fourier Transform plot).  For a parabola of the
> form:  P = a*f*f + b*f + c   (where P="power", f=frequency), the
> relevant PASCAL equations are:
> 
> true_frequency := -b/(2*a);    {the min or max of the parabola}
> sigma := sqrt( abs( (4*a*c-b*b)/(4*a*a*(N-1)) ) );

   Although I have not yet read that paper, the equation seems to be
understood when we try to solve P(f) = 0.  The denoted "sigma" is likely
to be a measure of the half width of the fitted parabola, extrapolated
to the zero signal level (P=0), then normalized by the degree of freedom
(probably assuming the deviation from the periodic signal is random and
uncorrelated).

   In the case of Fourier transform, this formulation seems to be verified
after some mathematical excercise (which I have not done yet ...).
The case of PDM seems to be harder to understand.  Since in PDM plot (theta
plot) the "zero" signal level corresponds to P(f)=1, it should at least
be solved P(f)=1, yielding

   sigma: = sqrt( abs( (4*a*(c-1)-b*b)/(4*a*a*(N-1)) ) );

   The second point I can not understand is what determines the width of
the valley of PDM plot.  Is ther the same rule as in Fourier transform?

Regards,
Taichi Kato

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