Mike Raiford wrote:

> It's amazing when you look at how your auditory system works. Your brain 
> essentially gets the Fourier transform of what you're listening to.

Be careful with that...

Audio systems generally represent sound in the time domain. The Fourier 
transform moves data from the time domain to the frequency domain. But 
humans don't hear sound in the frequency domain; they hear it in a 
*combination* of both domains - i.e., as a spectrum that changes over time.

You can take a 5-minute song and take the Fourier transform of it, and 
that will only tell you what combination of [fifty zillion] sine waves 
you need to add together to get back the same waveform. That's not how a 
human would perceive it; they hear notes and beats and things - sounds 
*changing* over time, but one static combination of frequencies.

It turns out this is one of the most tricky things in DSP. Working with 
signals that have a meaning in *both* domains...

(You might think, for example, that you could just snip your 5-minute 
song into, say, 50 ms chunks and take the Fourier transform of each 
chunk. Alas, snipping it up introduces phantom frequencies that aren't 
really there.)

I've spent a significant amount of time trying to come up with some 
mathematics for analysing sound the way that the human auditry system 
does... So far, nothing works.

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