I am trying to create a synthetic galaxy spectrum, by convolving a gaussian-velocity-distribution f(v) with my stellar spectra S. I have already logarithmically rebinned the spectrum and removed the continuum (see result in the lower plot below).
Now I want to broaden this continuum removed spectrum with a gaussian distribution, on paper I know what to do analytically:
Here G stands for the galaxy spectrum. My main problem is that I do not quite understand how to create my velocity space, since I have to define the broadening function f(v) there. In my implementation I have to perform the convolution of 2 numpy arrays (f(v) and S(ln(lambda)-v/c)), but in practice I do not know how to approach this. I apologize if this is not concrete enough and I will try to improve my question if desired.