I want to convert a simulated gain/absorption of a material, which can be understood as a discreet (dispersive?) function $g_i(f_i)$ ($f$ is for frequency) or $g_i(\lambda_i)$, into $\tilde g(t)$ for Finite-Discrete Time-Domain simulations. My title is actually almost the title of this paper where you can find the (mainly theoretical) details.
I know that a wide-band lorentzian algorithm can do the job and that I probably have to do a parameter extraction (based on an analytical solution of a corresponding system of non-linear equation) or somehing like this, but I don't know where to get or how to write the (complete) algorithm. I have MatLab and I can also code a bit Python and a bit C++.
Is there in MatLab a toolbox for this, can i use/how to use FIR/IIR-Filter
or other Convolutional Coding?
I don't really got the theory! Fit multispectral lorenz curves to my $g(f)$-data and do some magic Fourier-Transformation with filters, kernels and/or recursive convolution to get $g(t)$?
Does the Kramers–Kronig relations also play a role to convert the absorption/gain function to real refractive index, to fit over the complex refractive index function ?
I also read a lot of buzzwords but cannot connect them properly:
convolutional coding, (linear) recursive convolution procedure, FIR-Filter, (multispectral-lorentzian fit, kernel function etc...)