Frank's point is essential to understand how to decompose noise on a periodic waveform to amplitude noise or phase noise.

Quote:


We instinctively think of v_n(t) as "additive noise". This is not enough, because if we look at each spectral component of noise only, that is v(t)-v_n(t), it will decompose into half amplitude and half phase noise.

When we look at the physical mechanisms responsible for producing phase noise (J. J. Rael and A. A. Abidi, “Physical Processes of Phase Noise in Differential LC Oscillators,” in Custom IC Conf., Orlando, FL, pp. 569-572, 2000), then each spectral component of device noise produces a pair of correlated sidebands in the oscillator output spectrum. It is by examining the instantaneous phase of these sidebands relative to the oscillation that we can determine whether they are phase or amplitude noise.

Indeed, a spectrum analyzer can never tell them apart. Ultimately we must measure fluctuations in the zero crossings, which are unperturbed if the sidebands are correlated one way, but are perturbed if the sidebands are correlated in the orthogonal way.

So the right analytical method to extract a(t) and p(t) will, in effect, search for correlations in the sidebands of the spectrum of v_n(t).