POV-Ray : Newsgroups : povray.off-topic : A question of pure mathematics : Re: A question of pure mathematics Server Time
14 Nov 2024 23:21:04 EST (-0500)
  Re: A question of pure mathematics  
From: scott
Date: 20 Nov 2007 07:18:56
Message: <4742d0b0$1@news.povray.org>
> I read that back in 1997. (Yes, that's how old it is.) I had trouble 
> understanding it back then, and having reread it a few times since then, I 
> still have trouble comprehending it.
>
> I think essentially wavelets are just too complicated to understand. So 
> I'll stick with my original approach...

I don't claim to be anything like an expert on wavelets, but for someone who 
apparently knows about fourier transforms it goes like this (roughly):

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

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.

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.


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