Currently doing a maths project where I am trying to change sound into pure sinusoidal waves. I learned that the theory behind this (mathematical machine) is that there are complex sinusoidal waves which are the sum of pure sinusoidal waves, and that the shape of the wave is altered by wave interference (propagation), and that it should be possible to decompose. Originally I thought that the FFT filter would help me find these pure waves but I’ve learned that it doesn’t really help. Is anyone willing to help? Thank you.

@Trebor Thank you for the recommendation. I’m not sure if I can understand them, but I’ll try. Would you mind if I ask you what you do? (Or is that too rude?) (Like your profession, I’m just curious to what people use these type of software).

I’m not an expert and I’m not familiar with SPEAR…

In the real world FFT is “imperfect”.

Theoretical FFT (or DFT = Digital Fourier Transform) “assumes” (or requires) a continuous infinitely-long wave.

Audio FFT is normally “windowed”… Short sections of audio are analyzed and overlapped. If you look at the spectrum of a single frequency in Audacity you see a frequency range with a peak (it looks like a narrow bandpass filter). You’d expect a vertical line or bar from FFT with a pure sine wave.

A bigger FFT size (more samples) can give a better result. But real-world audio changes moment-to-moment so you have to make a compromise with music or speech.

FFT also gives results in frequency *bands* so you don’t get the exact-individual frequencies.

Noise reduction:

Inharmonic noise gets lost in translation after being converted to sines.

Representing sound as a series of sines can reduce the bandwidth needed to transmit it, (at the expense of fidelity).

Cochlear implants rely on this type of processing … What a cochlear implant sounds like to a single sided deaf individual - YouTube

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