The first one requires normalization so the trigonometric identities
can be utilized to find the phase and it also requires the frequency of
the signal to remain constant. The result being between -180 and
180 is just the result of the complex to polar function.
The second one determines the phase of each signal individually and
then subtracts them. If you want the same range of output, just
feed the phase into a polar to complex function (connect a constant
equal to 1 into r) and then into a complex to polar function. The
phase should then be in the -180 to 180 range.
This first approach assumes the phase is constant throughout the whole
sample, so you can think of the result being the average phase of the
whole data set. The second approach computes the phase at each
point and so it is much easier for error to creep into it since phase
is much more sensitive to noise. Since the first one is more of
an average phase, the sampling rate is not as significant (as long as
it is above Nyquist). I suggested a higher sampling rate for the
second one to minimize the jumps in phase from point to point, but
there will be a trade off with how much noise is introduced into the
system by sampling at a higher rate which will distort the phase.
Randall Pursley
