[time-nuts] windows for FFT measurements of phase noise

John Miles john at miles.io
Fri Jun 10 19:09:18 EDT 2016

> What sort of windows do folks use for making FFT measurements of phase
> noise.
> Say you have 1 second of sampled data (so the FFT resolution is 1 Hz).
> If you're interested in the noise power at, say, 10 Hz away, a
> rectangular window isn't going to be very far down, unless you have a
> LOT of points in the FFT.
> Grove's paper from 2004 doesn't mention this detail.

As Bob suggests, a multisegment FFT chain is the usual approach.  By the time you're displaying noise down to 10 Hz, you should have quite a bit more than 1 second worth of data to draw from. 

For measuring noise the choice of window function doesn't matter very much as long as you correct for the noise bandwidth of the function you use.  However, for spur detection there are major window-dependent differences that need to be considered.  There is only one reference that's worth looking at, and that's the paper by Heinzel, Ruediger, and Schilling.  (Google the authors' names and it'll come up.)  

The TimePod and 3120A allow the user to choose between the HFT95 function from the Heinzel paper -- which was essentially reverse-engineered from the HP 35670A -- as well as the usual (von) Hann(ning) window.  HFT95 is the default, with good sidelobe rejection and high amplitude accuracy for spurs regardless of where they fall in their FFT bin.  The Hann window can be selected when frequency offset accuracy and/or resolution of closely-spaced spurs is more important, but it can underreport their amplitude due to scalloping loss.  

I would suggest using one of the HFT windows unless/until you have a specific reason not to.  Heinzel also describes several flattop variants with higher sidelobe rejection than HFT95, in the unlikely event you need them.  In my experience it's better to stick with flattop windows and increase your bin density if you need better frequency resolution, rather than put up with scalloping loss.

-- john, KE5FX
Miles Design LLC

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