improve Lorentzian fitting for resonator spectroscopy with large background fluctuations

[RoyStegeman]

Currently peak detection in resonator spectroscopy is very naively done with min() or max() on the signal after a linear background has been subracted. In some cases the minimum or maximum of the spectrum may correspond to a variation in the background rather than the peak.

To account for this scenario we should at the very least use find_peaks rather than min or max.

[alecandido]

In some cases the minimum or maximum of the spectrum may correspond to a variation in the background rather than the peak.

Just to add some context, it could even be due to a slow varying background. Not necessarily an outlier in the incoherent noise.

This would happen if the background has a strong curvature, which is not fully captured by the linear subtraction.
If we could manage to segment the window (as attempted in #1497), this effect would be reduced.

Still, max() and min() are very noise-prone. Much better the peak detection anyhow

[alecandido]

Regarding the data in #1492 (comment), the simplest find_peaks() is already able to detect the peak itself

def scale(x):
    min = x.min()
    return (x - min) / (x.max() - min)

def peaks(y):
    peaks, info = signal.find_peaks(-scale(y), prominence=0.1)
    return peaks[np.argmax(info["prominences"])]

p = peaks(y)
plt.plot(y)
plt.scatter(p, y[p], color="red", marker="x")

I will try then with the segmentation algorithm. But this is already a hint that there is already some low-hanging fruit.

[alecandido]

And this is the segmentation from #1497. Exactly that notebook, just switching the data - no hyperparams fine-tuning

(the only difference is the first panel, which is not yet rescaled in #1497 - but it is just the raw data presentation, and the only difference is that the red cross has the correct height, relative to the signal)

However, I'm a bit disappointed, because the orange window here is clearly inadequate (too narrow), and the green one is required. But the green one is just a random guess, and it could be constructed directly on top of the red cross in the first panel.

The good thing could be that, for very narrow peaks, a random guess could be suitable. And (hopefully), for broad ones the orange one will instead work fine.
In this way, both regimes would be covered by the green window. But it is something that should be verified.