I want to do the FFT of an audio signal in real time, meaning while the person is speaking in the microphone. I will fetch the data (I do this with portaudio, if it would be eas
Real-time FFT means completely different from what you just described. It means that for given N and X[N] your algorithm gives Fx[i] while incrementing value i. Meaning, proceeding value does not compute until current value computation completed. This is completely different from what you just described.
Hardware usually uses FFT with around 1k-16k points. Fixed N, not real-time computation. Moving window FFT as described with previous answers.