Owen Duffy wrote:

Isn't hopping onto the rotor (assuming synchronous speed) to make your
observations called moving from the time domain to the frequency domain,
and all the mathematical shortcuts are only valid if all quantities share
the same angular velocity (or frequency), implying sinusoidal waveform.

I guess a departure from the strict phasor environment is for example
when we consider a noise vector rotating about the end of a carrier
phasor in exploring FM detector S/N vs C/N.

That's why it's essential to not forget the implied exp(j * omega * t)
term -- all waveforms in an analysis must include it, and it must be the
same omega for all. In addition to inherently non-sinusoidal waveforms,
waveforms resulting from any nonlinear operation, such as frequency
modulation or multiplying or squaring waveforms, can't be analyzed in
that environment.

Roy Lewallen, W7EL