The Sound of Harmonics - Approximating instruments with Fourier Series¶

In a previous article about the Fourier Series calculation we have illustrated how different numbers of harmonics approximate artificial periodic functions. The present post applies the results to the analysis of instrument sounds, namely sounds of a saxophone.

When playing a stationary tone on a saxophone, we hear a constant sound. Hence, we can assume its waveform is periodic, since we could start to listen to the tone at any time and would still hear the same tone. So, the waveform needs to repeat itself over and over again. In this case, it should be possible to expand the waveform into sines and cosines of harmonic frequencies and reconstruct the original signal from them.