I would like to extract a decaying exponential curve from another curve that I already have, which is known to be the result of the convolution of a Gaussian and the pre-mentioned decaying exponetial.
The exact form of the exponential is unkown, but the form of the gaussian is known relatively well (i.e. amplitude, Full-width half maximum), and could be decsribed by your standard gaussian equation.
The already convoled data is also known, though it is relatively discreet, with uneven spacing (e.g. X = [0 1 5 10 20 100 200 500 1000])
I have tried using the "deconv" function available in matlab (https://uk.mathworks.com/help/matlab/ref/deconv.html) to hopefully get this exponential out, setting u to be the vector related to the already covolved data (whose length is the same as X), and v to the gaussian curve calculated at the already mentioned X positions (and hence is of the same length as u). However, it does not produce an exponential as hoped, and now at a loss of how to proceed.
Any suggestions or tips as to how I may be able to achieve this would be greatly appreciated. Thanks.