niobium Posted February 19, 2006 Share Posted February 19, 2006 Anytime Actually, I did my master thesis on FFT, used for pitch-shifting. Is pretty much the same as time-stretching, since if you can timestretch perfectly, then you can pitch-shift perfectly - and vice versa. I made a realtime algorithm extending the SuperCollider language. Great fun, and I leanred ALOT of math in the process! -A 443317[/snapback] cool another math guy I am particularly interested in Orthogonal Series bases in infinite dimensional vector spaces / function spaces - so I am right keen on the Fourier stuff Quote Link to comment Share on other sites More sharing options...
furthur Posted February 20, 2006 Share Posted February 20, 2006 I am particularly interested in Orthogonal Series bases in infinite dimensional vector spaces / function spaces - so I am right keen on the Fourier stuff 443496[/snapback] hmm, doesn't ring a bell it has either been too long since a meaningful theoretic algebra course, or i might have not seen that at all, not a huge algebra buff myself, having majored in applied math, it was a choice between going further in analysis or algebra Quote Link to comment Share on other sites More sharing options...
furthur Posted February 20, 2006 Share Posted February 20, 2006 I know it's possible, I've heard music slow down and stop completely, without quality loss... -A 405403[/snapback] I have also heard that, and the quality only improved during those moments Quote Link to comment Share on other sites More sharing options...
niobium Posted February 20, 2006 Share Posted February 20, 2006 hmm, doesn't ring a bell it has either been too long since a meaningful theoretic algebra course, or i might have not seen that at all, not a huge algebra buff myself, having majored in applied math, it was a choice between going further in analysis or algebra 443730[/snapback] hehe, and I chose the other route the orthogonal bases for function spaces are an infinite but countable set of othogonal or even nicer orthonormal 'function basis vectors' A very relatable example is: Function Space >>> set of differentiable functions orthonormal basis >>> {cos(n*Pi*x)} for all integers n. This is the Fourier basis vector set. The meaning is that any differentiable function say from R >> R can be represented as an infinite linear combination of the cosine functions. There are tons of other polynomial sets and other things that can do this as well... Man some of the Analysis shit I studied was fascinating. One interesting result is a topological proof called the banach tarski paradox. Basically it says that you can cut up a grapefruit into six extremely complicated pieces and then reassemble the pieces into two grapefruits of the same size!! Quote Link to comment Share on other sites More sharing options...
furthur Posted February 20, 2006 Share Posted February 20, 2006 indeed, some topological results are wild Quote Link to comment Share on other sites More sharing options...
Amygdala Posted February 20, 2006 Share Posted February 20, 2006 One interesting result is a topological proof called the banach tarski paradox. Basically it says that you can cut up a grapefruit into six extremely complicated pieces and then reassemble the pieces into two grapefruits of the same size!! 443734[/snapback] Oh yeah, I heard that too! That's nuts to think about... Who comes up with this kind of stuf?!? Tarski, I guess My math skills aren't very impressive, but I was sort of forced to learn for my thesis. It was fun though, and it got more fun, the deeper I dug into it. It's so cool, that pure number-crushing can be used for aesthetic purposes. -A Quote Link to comment Share on other sites More sharing options...
niobium Posted February 20, 2006 Share Posted February 20, 2006 Oh yeah, I heard that too! That's nuts to think about... Who comes up with this kind of stuf?!? Tarski, I guess My math skills aren't very impressive, but I was sort of forced to learn for my thesis. It was fun though, and it got more fun, the deeper I dug into it. It's so cool, that pure number-crushing can be used for aesthetic purposes. -A 443776[/snapback] EXACTLY. the banach tarski paradom theorem has been refined down to five pieces now. it does happen to rely on an axiom of set theory that not all mathematicians are comfortable with. Another totally mindblowing result in Logic is Godel's 1925 paper of one page that single handedly destroyed the idea that mathematics was perfect or 'complete' Quote Link to comment Share on other sites More sharing options...
Amygdala Posted February 20, 2006 Share Posted February 20, 2006 EXACTLY. the banach tarski paradom theorem has been refined down to five pieces now. it does happen to rely on an axiom of set theory that not all mathematicians are comfortable with. Another totally mindblowing result in Logic is Godel's 1925 paper of one page that single handedly destroyed the idea that mathematics was perfect or 'complete' 443783[/snapback] Aaah yes... Gödel. I still remember the lecture where this result was proven (edit: obviously when it was proven to ME - I'm not that old, hehee). I hadn't really found the interesting core of computer science yet, but I had to sit 5 minuttes after that lecture, and just think - or just - hmm, the verbification of "intuition" That was a cool lecture - and a pretty darn nifty theorem. -A Quote Link to comment Share on other sites More sharing options...
niobium Posted February 20, 2006 Share Posted February 20, 2006 Aaah yes... Gödel. I still remember the lecture where this result was proven (edit: obviously when it was proven to ME - I'm not that old, hehee). I hadn't really found the interesting core of computer science yet, but I had to sit 5 minuttes after that lecture, and just think - or just - hmm, the verbification of "intuition" That was a cool lecture - and a pretty darn nifty theorem. -A 444341[/snapback] the man was brilliant. Paul Erdos had a saying: God has a thin little book containing all the theorems. I reckon Godel's proof would be in that book. one page. David Hilbert was blasted off his ass and HE was no slouch. Incidentally, Paul Erdos had MAJOR difficulty grasping the Monty Hall Theorem !!! Quote Link to comment Share on other sites More sharing options...
Amygdala Posted February 21, 2006 Share Posted February 21, 2006 Hehe, I reckon Paul Erdos is not exactly right -A Quote Link to comment Share on other sites More sharing options...
niobium Posted February 22, 2006 Share Posted February 22, 2006 Hehe, I reckon Paul Erdos is not exactly right -A 445337[/snapback] no, but it's a pretty little idea Quote Link to comment Share on other sites More sharing options...
Amygdala Posted February 23, 2006 Share Posted February 23, 2006 Yup - and imagine if it was "true" - then Gödel could prove god wrong. It wouldn't be the math and logic world that would be appaled if that was so -A Quote Link to comment Share on other sites More sharing options...
electric blue Posted February 23, 2006 Share Posted February 23, 2006 Well, that's a start. But, it is a given more or less that each channel has a Zx1 vector I assume right? Each component in the channel vector being a 'bit' (0 or 1) of course. Begin conjecturing ramble: 441606[/snapback] sorry for late response. yes each channel is a Zx1 vector, but each element in that vector should be a 16 bit or 24 bit (or 8 bit etc.. depends on the quality of your soundfile) number. Quote Link to comment Share on other sites More sharing options...
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