How to perform convolution with a dataset?

I have a dataset from an experiment and want to utilize it with the following equation that I have derived analytically

assume A , C, and D as any arbitraty numbers as their derivation is too long to put here along with beta and alpha (not of a concern now as i just want to understand how to implement convolution). while G is the values obtained from experiment as function of time. you do not have to demonstrate this particular one, you may supply your own example but I want to understand how to implement this in matlab with a dataset

Answer 1

[Bjorn Gustavsson]

In matlab this should be as simple as

f = A*(C*exp(alpha*t + D*exp(beta*t))); % or whatever you have for that part.
G = psf;  % Also given it seems
y = conv(f,G,'full'); % or 'same' or 'valid'

HTH

[Bourbon]

Yes G is a given, however, psf function is for point spread fuction of image system. In this case, I have G as a function of t in form of table (t, G). should I integrate G utilizing trapezoidal method prior to implementing convolution instead of psf? the data is quadratic in nature

[Bjorn Gustavsson]

conv (and conv2, convn) does discrete convolution and not a analytical/symbolic. If you have your G on a much finer grid than f, then it makes sense to recalculate G to the same discretization - that is: make sure that your dt is the same for G and f. After that everything is the same. (Also: psf is used for 1-D systems like spectrographs too...)

HTH