Extract Real and Imaginary Components of AC Signal

[Cannon_Controls]

I have recently been tasked with a project involving analyzing AC signals and it's been quite a while since I learned about these things in school. Essentially, I have 3 AC signals that I am acquiring and analyzing. I am calculating VRMS, Phase shift between signals, harmonic distortion, frequency, etc. All of this is working just fine. The part I am having a hard time with is calculating the phase angle of signals (not the phase shift between two signals). Basically, I need to break the waveform up into real and imaginary components in order to determine the phase angle. See attached image for an example. I've tried exploring some labVIEW functions that I haven't messed with before but haven't had much success. I am assuming I likely need to pass the waveform through an FFT but I am not sure exactly where to go from there. I was curious if anyone had any experience with this. Also, if there was some sort of toolkit out there that already had this capability, that would also be an option. I am fine to develop the programming myself. I really just need some guidance on the how to from an AC signals perspective. Any help would be greatly appreciated.

[altenbach]

I would start by attaching some typical data.

Are they mostly sinusoidal with one major frequency component (+noise) or more complicated

Are the three signals correlated?

[Cannon_Controls]

Attached is a file that contains the VRMS data from two of the signals during a recent test. The signals are all 3 sinusoidal. The dynamics vary from time to time but in this particular instance, we have an excitation voltage of 7.07 VAC at 3000 Hz. From there, we have two signal voltages. Va is about 3.1 Vrms and Vb is about 1.07 Vrms. While there is a very small amount of noise, we are generally only seeing the numbers bouncing around in about the third decimal place. If I need to apply some sort of high pass filter to better improve the effectiveness of an algorithm, I can figure that out on my own. These three signals are all correlated as the one is an excitation voltage and the other two are the measurement signals coming off of an LVDT. In regular usage, we have a phase angle voltmeter that we use for measuring the phase angle of the signals. We are trying to develop a lower cost and lower accuracy poor mans phase angle voltmeter that we can use for more mobile/ R&D testing. But yeah, the signals are very consistent in terms of Vrms and frequency. I really am just having a hard time breaking the signal apart into real and imaginary components in order to calculate the phase angle.