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

[Tijd Dingen]

Henk wrote:
> > Wavecrest uses algorithms for this and their software gives a spectrum.
> > They also give some info on their site.

Henk, the paper you mentioned put me on the right track. Thanks. :)


Magnus wrote:
> In "Jitter, Noise and Signal Integrity at High-Speed" by Mike Peng Li,
> Prentice Hall, ISBN 0-13-242961-6 it is covered in pages 200-207.

> It converts the phase jitter Phi(t) into the autocorrelation function
> R_Phi(tau) (equation 7.40) and then the phase jitter PSD can be estimated
> using the fourier transform (equation 7.41). The phase-noise can then be
> calculated using the standard L(f) = 10*log10(PSD(f)/2). It's pretty
> straight-forward.

While I don't have that book lying around here, going from the Wavecrest paper
Henk mentioned, I did find out that indeed the method is to calculate the
autocorrelation of the timeseries and then FFT this autocorrelation. The method
even has this easy to google name: Blackman-Tukey.

LeCroy has a paper with a short explanation that I found useful:

http://www.lecroy.com/files/WhitePapers/WP_TechBrief_Var_of_Time.pdf


> The autocorrelation processing is O(N^2) while the DFT can be done in
> O(N log N) when using FFT. As usual these can be implemented in reversed
> order such that first the FFT is done to the phase jitter and auto-correlation
> can be found using O(N) post-processing.

If it can be done in N log N that would be nice. :)

> The phase-noise measuring ability of the SIA-3000 I have is not competing with
> real phase-noise measuring sets. It doesn't say it can't be useful.

And what I am trying to do will probably not even compete with that SIA-3000.
It is more along the lines of...  Hey I have these times stamps anyway. Now what
can I do with those besides calculate a frequency estimate of the frequency 
under test?

Fred


 
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