# How to generate a sound closer to a saxophone using sinusoids after Fourier Transform?

Generate a sound wave of saxophone frequency and compare it to the original sound clip and play both to listen to if there is a good match.

I am trying to generate a sound closer to a saxophone using its Fourier Transform computation and picking apart different frequencies, building their respective sinusoids, and playing the resulting sound.

However, all of them are quite far from a saxophone. (I've found that a saxophone has a frequency range of 600 - 800 if I'm not mistaken). The last attempt is added below.

freqs = [250, 400, 1250, 1550]
amps = [1000, 20000, 5000, 5000]
phases = [0, 0, 0, 0]
[y_complex, t] = Synthesize(freqs, amps, phases)


(Synthesize is used to generate the respective signal from multiple sine waves at the respective frequencies and amplitudes)

Many tutorials available on the web for generating a guitar sound - e.g. https://www.youtube.com/watch?v=HEcdmDSVHsE, but the saxophone seems harder.

• You say "using it's Fourier transform computation" -- does that mean you have a clip of a saxophone, and have taken it's Fourier transform? If a saxophone (or anything else, for that matter) outputs a repetitive waveform, what will the relation between the frequencies of the wave's components be? Oct 11, 2022 at 2:13
• what is it about a saxophone that makes it sound like a saxophone? The sax player toots a single note and what do you have? Oct 11, 2022 at 3:31
• Exactly @TimWescott - I took it's FFT and I got its Magnitude plot. (Added now for frequencies between 100 and 2000) In the tutorial mentioned, the magnitudes repeat at specific intervals (E.g. 146.83 Hz), but in my case I don't know how to extract these repetitions. Oct 11, 2022 at 12:29
• @robertbristow-johnson an issue in my case is that the clip is part of a song - so the saxophone is just the main instrument, probably with the highest frequency. The highest magnitude I spotted was at 400Hz, so I tried to use more amplitude of that. If a single note is tooted, that would probably mean a single frequency (like in the tutorial) should come up? Oct 11, 2022 at 12:34
• I think you need to find or make a clean recording of a single saxaphone note. Failing that, assume that your biggest peak is the fundamental, and look at the tones just at multiples of that. "If a single note is tooted ... mean a single frequency". You could express it as a single frequency, a saxaphone note is pretty non-sinusoidal. So there will be overtones at multiples of the fundamental. Oct 11, 2022 at 14:51