Deconvolution Using Response to an Heavy Side

Question

I'm measuring a "charge" signal in function of time from an amplifier. Here is a measured signal (x-axis is the time in some arbitrary units, y-axis is the charge in ADU):

I would like to get the "true", original signal, by deconvolving the instrument's response from the measured signal.

Here the response of the instrument to an Heaviside step function:

I guess this should help me characterize the instrument's response, and do the deconvolution. I read about SVD and Bayesian unfolding, but these don't seem to do the trick (I need to built a transfer matrix first). Could you suggest me any tool/algorithm to do this?

Thanks in advance for the help.

Answer 1

If we can assume no noise (Or the SNR is very high) you can get the response by applying the inverse filter in frequency domain.

Lets say $ y [n] $ are the signal samples.
Given $ x [n] $ the samples of the ideal signal you can apply on both of them the DFT to get $ Y [k] $ and $ X [k] $.

The response is given by the Inverse DFT of the division $ \frac{Y[k]}{X[k]} $.

If there's some noise you need to regulate the result.
Easy choice would be the Wiener Filter or more specifically Wiener Deconvolution.