Method
Differential capacity underpins most incremental-capacity work, and it is also the plot ordinary cleaning ruins most easily. The mechanism is simple, and worth understanding once.
Mechanism
Differentiating a noisy signal amplifies the noise, and the amplification grows as the spacing between samples shrinks. A voltage trace that looks perfectly usable turns into a dQ/dV curve where the noise reaches the height of the third peak.
The first instinct is to smooth the result until it looks like the figure in the paper you are comparing against. That is where the trap is.
Any symmetric smoother applied to an asymmetric peak drags its apex toward the heavier shoulder. dQ/dV peaks are rarely symmetric, so the apex moves — usually by a few millivolts, which is exactly the scale at which people read phase transitions.
What makes it worse is that the result looks better. A smooth curve with a displaced peak gets published more readily than a genuine peak buried in noise.
What to do
If smoothing is needed, apply it to the voltage and capacity traces before differentiating — and write down that you did. The distinction matters because anyone can check it.
Sorting to force a monotonic curve produces a tidy plot and destroys the order in which the measurements were taken. After that, any conclusion about rates or sequence is meaningless.
Plot the original and the cleaned dQ/dV on the same grid and compare peak positions. If the apex has moved and you cannot say by how much, it is not yet clear whether your conclusion is about the cell or about the filter.
What a defensible workflow records: whether smoothing happened before or after the derivative; the method and its parameters; the evaluation grid — voltage bounds, step, interpolation, trimming; peak positions before and after with the shift; and which ranges were excluded from peak claims, and why.
Start
Free, in your browser, before anything is smoothed — ninety seconds is enough to see whether this problem applies to your data.