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> It's certainly not something you can simplify down to just the component sinusoids. Anything a human can perceive as sound can be simplified down to just the

> It's certainly not something you can simplify down to just the component sinusoids. Anything a human can perceive as sound can be simplified down to just the component sine waves. > You can say we perceive things as if they were a linear combination of sinusoidal waves because we have a series of hair cells in the cochlea. No. We say this because any waveform can be reproduced by a sufficient number of sine waves at different frequencies and amplitudes. It's not perception, or the physics of the human ear. It's math.[1] [1] http://astro.pas.rochester.edu/~aquillen/phy103/Lectures/D_Fourier.pdf http://astro.pas.rochester.edu/~aquillen/phy103/Lectures/D_F...

hwillis 6y ago
Hah, I graduated from UofR- I was even a TA for Physics 142. Math does not have anything to say about sums of sine waves being the true form of functions. The wavelet transform is just as physically representative. In fact you can generate any number of Hilbert bases for a given function. They are ALL equivalent. The Fourier transform has a particular relevance because ears do something similar. Hair cells signal the brain while they are sensing vibrations within their particular frequency range. You could have different ears that signaled when they saw a sharp rise or drop in pressure and worked completely differently, but they would sense square waves just as fine. Or you could have ears that directly sense and measure air pressure. Instead, our ears sense that there are vibrations at 1 Hz, 3 Hz, 5 Hz, 7 Hz etc. and the brain interprets that and realizes it is a square wave. The concept of a real Fourier transform is just as unphysical as a real square wave. A real Fourier transform requires a perfectly defined sound pressure at every instant; because air and sensors have inertia that is not possible. There will always be lag, so any change in frequency is not perfectly transformed or represented from/as a sum of sine waves.

hwillis 6y ago

Hah, I graduated from UofR- I was even a TA for Physics 142. Math does not have anything to say about sums of sine waves being the true form of functions. The wavelet transform is just as physically representative. In fact you can generate any number of Hilbert bases for a given function. They are ALL equivalent. The Fourier transform has a particular relevance because ears do something similar. Hair cells signal the brain while they are sensing vibrations within their particular frequency range. You could have different ears that signaled when they saw a sharp rise or drop in pressure and worked completely differently, but they would sense square waves just as fine. Or you could have ears that directly sense and measure air pressure. Instead, our ears sense that there are vibrations at 1 Hz, 3 Hz, 5 Hz, 7 Hz etc. and the brain interprets that and realizes it is a square wave. The concept of a real Fourier transform is just as unphysical as a real square wave. A real Fourier transform requires a perfectly defined sound pressure at every instant; because air and sensors have inertia that is not possible. There will always be lag, so any change in frequency is not perfectly transformed or represented from/as a sum of sine waves.