I have used FFT many times, but for real, non-periodic signals I consider it a poor estimator.
For most of my applications I am only interested on the power spectrum, so I use the Welch's method. I really like its approach to take overlapping segments, apply a window to each of them, calculate the FFT and finally average the result to get the power spectrum estimation. The method is easy to understand and its results are smooth and stable.
However I have one application that I am also interested in the phase of the signal. In fact am not interested in the phase estimation of particular signal segment, I want to see how the phases of very similar spread spectrum signals vary over time.
My signals spectrum are spread, but they always have a peak in the PSD, however this peak frequency varies over time. I will probably only need to trend the phase related to the frequency of this peak.
1) Does it make sense to use Welch's method for magnitude and phase, instead of power? I mean average magnitude and phase, instead of power.
2) Is there any magnitude and phase spectrum estimator that is smooth/stable like Welch's method?