Note: FFT only works with a sample count that is a power of 2, for example, 512.
And it assumes the waveform is periodic, i.e. after sample 511 (in the case of 512 samples) comes sample 0. That most likely implies a level jump, which will cause inclusion of a lot of harmonics that are not actually in the original sound. Think: sawtooth, for an original gentle slope, which includes all harmonics(even+odd) at an amplitude level 1/n. There are ways to reduce that effect, for example doubling the sample count while mirroring the original samples backwards, turning the sawtooth into a triangle (odd harmonics only, amplitude 1/nē, which is a lot better). Even more advanced systems can make using of windowing functions, adding original samples from the left and right, to the side, which gently fade in/out.
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