[time-nuts] Plot phase noise spectrum from DMTD measurement?

Magnus Danielson magnus at rubidium.dyndns.org
Sat Mar 12 09:39:07 UTC 2011

```On 03/11/2011 09:33 PM, Stephan Sandenbergh wrote:
> Hi,
>
> Ok some cool advice - this thread is an interesting thought exercise. I'm
> going to think about it a some more, but it seems, in comparison at least,
> the loose phase-lock technique remains the simplest. Provided you have a
> low-frequency spectrum analyser handy.
>
> The sound card idea is clever as well - however, I'd assume one needs to
> measure the ADCs clocking oscillator offset, since that will be apparent
> when plotting the beat frequency phase (what I mean is that sampling will
> then look like another mixing process). What I usually due is  to clock the
> sampling system off a clock that's correlated to the clock under test. This
> resolves that issue.
>
> However, I'd like to experiment with the cross-correlation idea, since I've
> got a setup that will lend itself perfect to that. Maybe I could save myself
> some time, with clever post-processing.
>
> Can anyone recommend a fundamental text on the cross-correlation technique?

Cross-correlation processing doing the hard way would involve N^2
multiplications but you can process it.

However, this is now done using FFT so what you do is...

Grab the two signals x(t) and y(t) from the two arms of the
cross-correlation receiver... (you want them to be sampled at the same time)

You then FFT transform them into their frequency variants X(f) and Y(f)

To get the cross-correlation spectrum you now do (for all f)

C(f) = X(f) * Y(f)*

The Y(f)* is the Y(f) with the imaginary term inverted.

If you have use for the cross-correlation time-series (usually not
needed for phase-noise) then using an IFFT to transform C(f) into c(t)
can be done.

This processing takes a few tens of lines C-code using FFTW as a FFT
library (recommended).

You can then average a number of these cross-correlation spectrums to
further suppress noise.

Remember that you will need to scale the result for proper dBC/sqrt(Hz)
which is connected to the carrier strength, sample rate, and FFT length.

Cheers,
Magnus

```