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

[Mark Kahrs]

The Goertzel algorithm is only useful when you want a few frequences
(i.e., it evaluates specific frequencies on the unit circle).  For
general all purpose slicing and dicing, the FFT is what you want.  See
the ancient book by Rabiner for the details.

On Tue, Feb 8, 2011 at 3:14 AM, Tijd Dingen <tijddingen at yahoo.com> wrote:
>
>
>> > 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.
>
>> Just knowing the time of the zero-crossings is very little information
>> to go by, but you have to make some kind of assumption about the
>> perfection of curve shape between those points, in order to say
>> anything meaningful.
>
> Correct. And for now the working assumption is that the input signal is
> sinusoidal, with just a smattering of noise.
>
>> The dirty but not necessarily quick way to analyze the data, is to
>> turn it into a +/- 1 squarewave at 1GHz (1/1ns), low-pass filter
>> it with a 15-18 kHz cut-off and do the usual FFT.
>
> Yeah, I thought of that one. But it becomes prohibitive in terms of resources
> real fast. ;)
>
>> The other option is to normalize your zero-crossings, so you get
>> signed numbers telling how early/late they happen, and do a FFT
>> on that.  Its too early in the morning for me to be able to see
>> how you transform the resulting phase-deviation spectrum to a
>> normal frequency offset plot, but a few tests with synthetic data
>> should tell you that.
>
> There's an idea. I will be doing a curve fit of the time stamps anyway, so I
> get the time deviations from the fit for "free". Normalize the time deviations
> into
> phase deviations, and use that. Worth a try, thanks!
>
> Fred
>
>
>
>
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