I agree, FFT is simply a correlation of a bunch of sine waveforms. The extra tidbit - the sine waveforms are orthogonal to each other (their cross correlation

I agree, FFT is simply a correlation of a bunch of sine waveforms. The extra tidbit - the sine waveforms are orthogonal to each other (their cross correlation is zero), so the transform can be inverted. (in math terms: they form a basis set. I'm mostly referring the STFT here, which is the 'common' FFT use. not infinite FFT).