https://stackoverflow.com/questions/15360214
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RussianWhen the data in the FFT is represented as Real and Imaginary components (this is the usual result of the FFT), just add the two together.
Adding the FFTs is just like adding the waveforms, which is what a chord would sound like.
If your FFT data is represented as Magnitude and Phase, you would need to convert back to the Real and Imaginary representation before doing the addition.
Also, in the comments, people have suggested that you can just add the magnitudes. The result of this will be a very different waveform than if you were to add the actual waveforms (like in playing an actual chord), or the FFTs, but the idea behind this is that the ear is completely insensitive to phase. I don't think this is true, and it's no easier than directly adding the FFTs, so why make this approximation? The only reason I could see is if you actually only have the spectra (typically meaning the FFT magnitude), but if you actually have the FFTs, I'd just add them. If you do add the spectra, make sure you're not looking at the square (which is typically what would be meant by power spectra), or log, etc, but the actual magnitude.
