maybe i can write formula for the two different sides, and their equivalence
indices * frequencies = indices * frequencies the sampling indices are arange(N) the recording indices are (arange(N) * (N * 2 - 1) / (N - 1)) % N since everything is exp(2 pi i * index * freq), indices * frequencies is taken % 1, because sinusoids are % 2pi. only the fractional component of indices * frequencies matters. ...
