[time-nuts] Calculate spectral content from a series of zerocrossing time stamps?

[J. L. Trantham]

DFT?  Direct Fourier Transform?

Thanks,

Joe

-----Original Message-----
From: time-nuts-bounces at febo.com [mailto:time-nuts-bounces at febo.com] On
Behalf Of Tijd Dingen
Sent: Monday, February 07, 2011 9:02 PM
To: time-nuts at febo.com
Subject: [time-nuts] Calculate spectral content from a series of
zerocrossing time stamps?




Consider the following scenario. We have a signal source of about 10 kHz,
with unknown phase noise. Let's for simplicity's sake assume for now that
the phase noise is large enough that it will be detectable by the following
approach.

We measure every zero crossing with lets say 1 ns accuracy. So we have a
signal with a nominal period of 100 us, and we can measure every zero
crossing to within 1 ns. This gives you ~ 10,000 data points every second.

Now how does one efficiently calculate the spectral content based on these
10,0000 zero crossings? The end result would be the spectral density,
centered around that nominal 10 kHz frequency.

>From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki
that extirpolates the unevenly timed samples to an regular timed mesh, after
which a regular DFT is done.

This is a nice enough approach, but you pay a computational price for the
fact that this algorithm is able to handle more generic inputs than is
needed in this particular case. So possibly there is a more efficient
method, only which one?

Any suggestions for methods/papers/etc are appreciated. :-)

thanks!
Fred



      

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