I am creating a spectrum analyser to visualize some stereo audio data in real time. I want to display a single spectrum for the input and a single spectrum for the output. The stereo data is the usual two channels: left (L) and right (R).
I am combining them into a single channel by taking the FFT of L + R. Is this conventional or would it be more appropriate to combine FFT(L) + FFT(R) rather than use FFT(L + R).
Also if I encode the left and right channels as mid (M) and side (S) do some processing on each of M and S and convert back to L and R then I observe the following:
If the side channel is modified, then taking FFT(L + R) shows no visible difference between the input and output (because L + R is pretty much the mid channel without side) so the question is: is there a way to combine the mid and side channels together so that taking the FFT of them gives a good representation of the sound. Or should I be doing FFT(L) + FFT(R) for both L/R and M/S processing modes? I would rather not have to do two FFTs if one would suffice.