Fitting fixed number of complex exponentials to complex signal I have a complex data series, and I would like to fit a fixed number (in this case, two) of complex exponentials of the form $Ae^{jBn}$, where A, B are complex. Not interested in the phase (i.e. arg of A), just its magnitude, and mainly the complex frequency. Target length is maybe 100 samples.

I would like to be able to capture the periodic destructive interference as the addition of these two fitted complex exponential signals.

Complex time-series in 3D:



I have looked into Prony-type methods and noise subspace methods, but I'm at a loss as to what is applicable here.
Complex A and B are a bit messy. What about using the signal model

$$ f(t) = \sum_{k=1}^{2} A_k\, e^{j(w_k t + \phi_k)} $$

where $w$ is the frequency and $\phi$ is phase.

Since sinusoids are orthogonal, probably the easiest thing to do is to Fourier transform the signal and pick out the two largest peaks in the positive part of the spectrum. These will correspond to the two main sinusoids.