# Phase of PM signal

Given two signals: s1 is a baseband frequency modulated signal (output of a frequency modulator, FM) and s2 is a baseband phase modulated signal (output of a phase modulator, PM).

I want to compare these two modulators: FM and PM. I need to compute phase imbalance. The first signal is frequency modulated, can I calculate the phase of this signal as for a phase modulated signal?

Phase computation (PM): $$\phi = arctan (I/Q)$$

EDIT 1.

I work on GMSK modulation. It is nonlinear, by using Laurent decomposition I can represent it as a sum of amplitude modulation pulses ( linear GMSK). Linear and nonlinear modulation were simulated. I want to compute the phase difference between baseband output of the modulators.

Deep space communication standard gives a phase difference limitation in term of phase imbalance (5°)

EDIT 2 Calculation I use

Linear modulation is a frequency modulation ( FM), nonlinear is phase modulation ( PM).

FM signal - $$s_{FM}$$

PM signal - $$s_{PM}$$

Phase of $$s_{PM}$$ was computed. It is output of the integrator, filter(1, [1,-1]. x), where x - result of convolution rect-function with Gaussian filter.

Phase of $$s_{FM}$$ was computed by using Matlab function angle and arctan2:

$$\phi_{FM} = \arctan (\frac{real(s_{FM})}{imag(s_{FM})}$$

In Matlab: angle(s_{FM}) and arctan2(s_{FM})

If I use the same calculation for $$s_{PM}$$,I will get another values, which are not equal to output of the integrator. (I asked here about it )

EDIT 3 Honestly, I am not 100% sure how phase imbalance was computed. I have found the value of it here , p 77 in pdf.

But I assume it is a phase difference between "ideal" case and approcimated.

• Hi! I'm not aware of the term "phase imbalance" used outside of mixers, so how does it apply here? Also, phase is phase, you always compute it the same way. So, that answers your question. Commented Apr 21, 2022 at 11:36
• Please make sure to not confuse the properties of a signal with the way it's generated. Phase is really just the argument of the complex signal; that's it. Commented Apr 21, 2022 at 11:45
• Here it was explained how I can compute an amplitude imbalance. Honestly, I have never used this "imbalance"... usually I compute a deviation (difference between two values). In deep space communication standards phase and amplitude deviation is given in “imbalance”. Commented Apr 21, 2022 at 12:16
• @MarcusMüller, "Phase is really just the argument of the complex signal; that's it" it is not important if it FM or PM signal, right? I can compute a phase of them via artan? Commented Apr 21, 2022 at 12:17
• Ok, now I'm even more confused. That post is about something you call "data imbalance"; "phase imbalance" is a term typically used for mixers, as mentioned above. (Usually, phase imbalance involves I and Q not being perfectly orthogonal, or at least different in gain.) Please, add the actual formula for what you call phase imbalance to your question. I mean, nobody calculates a number just for the fun of it, you want to do something with that, right? So, you have a formula that stems from an understanding of that purpose, please share it with us! Commented Apr 21, 2022 at 12:20