Fourier...stuff...
Author
Alright, so I'm currently taking a Pre-Calc equivilant course in high school(in New York, they give them dumb names, and mix up what you learn when a little, but it's basically the same...). For this math fair of ours, e have the option to write a paper for extra credit. I decided to do mine on Fourier Series/Transforms.
I've been looking around Mathworld, and Wikipedia, as well as various sources on the internet, but I just don't seem to get it very well. They use jargon, and tons of technical terms, that seem to hide the point.
Luckily, my dad has a pretty good grasp of Math, and he's been helping me through it, so I get the general Idea behind Fourier Series, but I don't get the actual details. Anyone have any help?
(Side Note: I'm trying to write my report on both Series, and Transforms(when I chose my topic I wasn't fully aware how different they were). Do you guys think I'd be able to write an essay on both, and cover both in enough detail? And if so, any good resources on Transforms that don't use so much jargon?
If you don't know calculus and complex numbers, you're pretty screwed really. Sorry, but both use calc and complex quantites extensively.
I did see a pretty good introductory article to FT's though, I'll see if I can find it.
I did see a pretty good introductory article to FT's though, I'll see if I can find it.
Just focus on one. The Transform has more interesting technical applications; the Series are more theoretical/mathematical. Doing both is too much.
For the transform, and especially the discrete version: the Fast Fourier Transform, there's all kinds of cool applications in sound and image processing, because it offers an efficient way to implement convolution. Convolution, in turn, is one way of expressing filters -- it's like sliding a long vector dot product along the input data stream and recording the output of that dot product at each step. For audio, you can do Eq, reverb, delays, phasers and other cool effects using convolution, and FFT is the fastest way to actually calculate convolution for block size 64 or higher.
Umm... well, at least I hope you got some related things to google for and put it all in context. The discrete world (where you have actual applications) and the math world (where you have the function series) are somewhat separate, though.
For the transform, and especially the discrete version: the Fast Fourier Transform, there's all kinds of cool applications in sound and image processing, because it offers an efficient way to implement convolution. Convolution, in turn, is one way of expressing filters -- it's like sliding a long vector dot product along the input data stream and recording the output of that dot product at each step. For audio, you can do Eq, reverb, delays, phasers and other cool effects using convolution, and FFT is the fastest way to actually calculate convolution for block size 64 or higher.
Umm... well, at least I hope you got some related things to google for and put it all in context. The discrete world (where you have actual applications) and the math world (where you have the function series) are somewhat separate, though.
Folks,
For the record, though this is school related, I'm allowing the thread to remain open since HemoGloben isn't asking for an answer to a stated problem. I really should revise the Forum FAQ to clarify that requests for guidance on how to learn about a particular subject, even when school related, is acceptable. Besides, Fourier series, etc., are in general on-topic for game math/physics.
For the record, though this is school related, I'm allowing the thread to remain open since HemoGloben isn't asking for an answer to a stated problem. I really should revise the Forum FAQ to clarify that requests for guidance on how to learn about a particular subject, even when school related, is acceptable. Besides, Fourier series, etc., are in general on-topic for game math/physics.
Author
Hmm....alright. Thanks guys.
Don't you have to know Fourier Series in order to know Fourier Transforms? Or are the two related only by name?
Don't you have to know Fourier Series in order to know Fourier Transforms? Or are the two related only by name?
It'll be pretty cool if you can learn it in high school. Will save you a lot of trouble later on in University. However the stuff DOES require a lot of calculus\linear algebra background, you won't master the topic without having the most fundamental skills.
If you have the time, at least read about the required stuff. Those jagons you mention are actually the most effective and correct way to express mathematical concepts.
If you have the time, at least read about the required stuff. Those jagons you mention are actually the most effective and correct way to express mathematical concepts.
Author
So what would you suggest, I just go to Mathworld, and work my way backwards through the Jargon until I hit something I know, then work forward?
Hmmm....suppose I could try that...maybe I'll talk to my math teacher...though she really doesn't like me....hmm...oh well.
Hmmm....suppose I could try that...maybe I'll talk to my math teacher...though she really doesn't like me....hmm...oh well.
Quote:Original post by HemoGloben
So what would you suggest, I just go to Mathworld, and work my way backwards through the Jargon until I hit something I know, then work forward?
Hmmm....suppose I could try that...maybe I'll talk to my math teacher...though she really doesn't like me....hmm...oh well.
id recommend strongly against using mathworld. its really not geared at all toward highschool students, actually, sometimes i think the people its geared towards would never need to look up anything anyway.
the link posted by python_regious is a excellent start. you can always dig deeper into the math afterwards.
Author
Thanks everyone.
Ironically, I've seen that link before, but I was in Algebra back then, and didn't really get any of it. But I totally forgot about it when I was looking for it recently.
So thanks python_regious, because it's exactly what I was looking for.
And thanks for allowing it to stay open grhodes_at_work. But now that I've found what I need, the threads fine to be closed if you'd like.
Thanks again.
Ironically, I've seen that link before, but I was in Algebra back then, and didn't really get any of it. But I totally forgot about it when I was looking for it recently.
So thanks python_regious, because it's exactly what I was looking for.
And thanks for allowing it to stay open grhodes_at_work. But now that I've found what I need, the threads fine to be closed if you'd like.
Thanks again.
This topic is closed to new replies.
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