hello
in theory, the sinus would be displayed as vertical lines in frequency domain
but numerical fft will introduce several leakages :
1/ for continuous signals, the fourier transform impose to apply a window to each buffer so that the signal start and stops with zero amplitude . This window will generate "side lobes" efffects in the frequency plot , so what you see in your graph is that side lobe effect on the vertical lines.
There are many type of windows depending of what precision you need on amplitude and frequency resolution / selectivity (minimization of the side lobe). it's all about trade offs.
2/ the f (frequency) vector is discrete , not continuous. As the frequency of your input signal will probably never match exactly the (nearest) frequency bin of the f vector. To reduce that , reduce the frequency resolution => you should increase the length of the fft buffer; but at the best you can only do one fft computation with a buffer (= nfft length) equal to the entire signal length. We we split a longer signal in smaller buffers and do averaging, it will increase the signal to noise ratio but decrease the frequency resolution by the same amount.
3/ now log vs lin scale.
usually, everybody doing spectral analysis use log (dB) vertical scale. That allows to see tiny amplitudes beside larger / dominant peaks. A graph with a vertical scale of 120 dB allows you to see two sine waves with a huge amplitude ratio of 1 to 10^6 (so for example 1 V and 1 microV can be seen together)
if you would use a linear scale, you would have trouble to see anything that is lower than 1% of your dominant signal.
so it's all about what you are looking for / or wanting to show / hide in your graphs.
