>If this was frequency modulation then a waveform may look like
>$ sin((\omega_0+f(t)) t )$
yes. well the QBO oscillations have of course a little fuzzy frequency component, but I wouldn't call this
"frequency modulation." And strictly speaking the QBO is even not really periodic, but only somewhat and the amplitude goes also quite wild. What I mean is, as said here
that it looks as if the signal is mostly having a strict two year period (i.e. I mean by that f(t) comparatively small) but once in a while not - i.e. it gets out of sync. Moreover it looks as if it is "forced back" into the biannual rythmn. I could imagine that this "out of sync" (disturbations, breaks) and forced back behaviour in an oscillation is rather well distinguishable from a more random behaviour via a fourier transform
but may be not and even if this would be so I don't know how the corresponding typical forms would look like.