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# Fourier series watch

1. How can i found the Fourier series from the waveform of a clarinet? where i know the harmonic, amplitude and Hz
2. (Original post by giometto)
How can i found the Fourier series from the waveform of a clarinet? where i know the harmonic, amplitude and Hz
I think what you mean is that you have a real wave recording from a clarinet and you want to replicate the wave using a generating function in the form of a Fourier sum.

To do this you would need to create a numerical solution where your unknowns are the coefficents in the Fourier sum and you set up an equation for each coefficient you wanted to find. You would do this from the fact that you could look at the physical wave form and equate the amplitude of the waveform at a particular time to the Fourier sum at this particular value of t.

You would need to guess at how many value of t to use and see whether the result bore any resemblance to the original sound.

This is a difficulty computational problem for which the Fast Fourier Transform algorithms will be your friend as these algorithms shorten the time needed to solve the equations that you will have to solve.

My guess is that you will need a lot of terms (thousands) to manage anything at all as real instruments have an enormous number of degrees of freedom in which to make sounds.

This may help
https://sooeet.com/math/online-fft-calculator.php

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Updated: January 30, 2017
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