scott wrote:

> If you do a normal FT on a signal, you get a nice graph of amplitude 
> against frequency.

But, sadly, only for a sationary siganl.

The problem, essentially, is that standard Fourier theory lets you look 
at a signal purely in the time domain, or purely in the frequency domain 
- but humans perceive sounds in *both* domains simultaneously.

> If you have a longer signal (eg a song) then you can split it up into 
> chunks and do FT on each chunk.  You then get a nice 3D graph of how 
> amplitude against frequency changes over time.
> 
> The problem is that the shorter you make the chunks, the less accurate 
> the frequency information is.  The longer you make the chunks, the less 
> accurate the time information is and the (more accurate) frequencies get 
> blurred together over time.

Or rather, the problem is that if the chunk bounderiess don't line up 
nicely with wave cycles, you get spurious high-frequency components 
being reported that don't actually exist in the original signal.

> What wavelets do is allow you to use a different chunk size for 
> different frequencies.  In a song you probably want a small chunk size 
> for high frequencies (the absolute frequency is not so important, just 
> the timing), and a large chunk size for low frequencies.

Yeah. I get all that. I just don't understand how the maths works.

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