How to plot "fitted" fourier transform

Hello everyone, I am a student MATLAB user and I need help with graphing some electrophysiology data. I am drawing a blank on what the graph I want to plot is called, so I am going to make up the term "fitted fourier transform". Here is what my fft plot currently looks like:

I want it to look like the red and green lines here:

I have 16 sets of data that I have to plot on the same graph (only two are shown), and they currently overlap to the point that I can't tell what sets have what amplitude. If I were able to plot the "fitted" data, I wouldn't have as much of a problem. I didn't outline the 60 Hz frequency, but it would be fine if that was in the new plot. I'd appreciate any help.