# Is it possible to recover the original signal from an LC circuit?

I'm using some photo detectors called Silicon Photo-multipliers (SIPMs) which produce a signal like the following:

Now, I take this signal and pass it through an LC circuit to get the following result:

Now, my question is: is it possible to recover the original SiPM pulse, given that the only thing that I have available is its LC output?

Note: those are not the precise fits for my pulses, that's just an example of what they look like. I can post the actual signals, if required.

• Great question, sorry I forgot to include it in my original question. I take the envelope of the SiPM pulse after the initial spike and then subtract that with the envelope that I fit to the peaks of the LC oscillations. I then use this subtracted result to obtain the original SiPM pulse by adding to the LC oscillations. This works for this particular case, but when I vary the amplitude of the SiPM pulse and hence of the pulse passing through the LC circuit, the same subtracted result doesn't give me the original pulse back. Instead of subtracting, I tried dividing too, but that doesn't work – Always Learning Forever Jan 17 '19 at 18:17
• that's interesting. You do not have mathematical equations of the exact waveforms. But in case you had, why not trying frequency domain methods? And also when you say LC circuit, you actually mean RLC right? So your filter response is invertable. – Fat32 Jan 17 '19 at 18:29
• Well, all of this is stemming from frequency domain multiplexing. I send in a signal through an amplifier and then through an RLC circuit. But how do I get the original signal after it passes through the RLC circuits and makes oscillations? How do I invert that filter response? – Always Learning Forever Jan 19 '19 at 1:30
• @Fat32 If I pass the signal through an RLC filter, how do I invert it? – Always Learning Forever Jan 21 '19 at 20:33
• if your RLC circuit is extrmely narrow band; i.e. an ideal LC with R going to zero, then inverting could be under heavy numerical stress... is it so? can you indicate the bandwith of the signal at the input of the RLC filter, and values of R,L,C components. ? – Fat32 Jan 21 '19 at 22:14