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

Magnus Danielson magnus at rubidium.dyndns.org
Wed Feb 9 22:33:03 UTC 2011


On 09/02/11 23:08, Tijd Dingen wrote:
> 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. :)

It's a reason why FFT has become so popular...

>> 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?

Knock yourself out.. :)

Cheers,
Magnus




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