Topic: fourier integrals
started by: CatKnight
Posted by CatKnight on Apr. 19 2002,04:31
they take so god damned long and are hard to do! does anyone (kuru) know an easy step by step method way to do them? basically I am just solving for a0, an, and bn, but those integrals take a while especially if f(x) is complicated.btw why do you sometimes use am and bm instead of an and bn?
Posted by Wiley on Apr. 19 2002,05:03
I would love to help you out, but I don't know what the fuck you're talking about. Sorry. 
Let me know if you need any info on good strip clubs in the LA area though.
Posted by Uberkommando on Apr. 19 2002,05:43
| Quote (Wiley @ 18 April 2002,23:03) |
| Let me know if you need any info on good strip clubs in the LA area though. |
Now's *there's* some knowledge you can apply.
Posted by damien_s_lucifer on Apr. 19 2002,10:21
and for that matter, will someone teach me the basics of the Fourier Transform? I have no idea how it works, but I know I need to know it if I'm ever going to program really cool audio.
Posted by kuru on Apr. 19 2002,13:18
CK, I haven't seen a fourier equation in .. um.. lessee, it was 1999 so that would make it 3 years ago.
Sorry dude, those are not on my plate anymore and I sold my calc books.
Posted by Wiley on Apr. 19 2002,14:59
See ...you'll never use this stuff in real-life. This is just stuff thought up by Da Man to keep us down! Fight back, read comic books instead of calc books ...your (illegitimate) kids will thank you for it.
Posted by Nikita on Apr. 19 2002,15:32
I decided to spare my brain cells and a few tree's worth of paper, so I took that class Mathematica. 
Posted by kuru on Apr. 19 2002,15:59
I could dig out my notebooks, I know I have those. That'll have to be done at home, though.
Posted by Necromancer on Apr. 19 2002,16:16
not knowing exactly how you've been taught it makes things harder. But still i can't really see any short cuts that could be used really. Using integration by parts is the only thing i can really see but i seriously doubt you havent been taught how to use that already when solving a fourier series.They're just a pain in the ass really. They most likely won't put a killer integration on your exam paper.
Posted by Necromancer on Apr. 19 2002,16:54
| Quote (damien_s_lucifer @ 19 April 2002,10:21) |
| and for that matter, will someone teach me the basics of the Fourier Transform? I have no idea how it works, but I know I need to know it if I'm ever going to program really cool audio. |
you do ridiculously longwinded integrations just to make a wave that looks square or spikey.
Posted by damien_s_lucifer on Apr. 19 2002,22:17
| Quote (Necromancer @ 19 April 2002,08:54) |
| you do ridiculously longwinded integrations just to make a wave that looks square or spikey. |
nah, I don't need to know all the steps involved, I'll just feed the data off to a Fast Fourier Transform algorithm and let it crunch everything for me.
What I need is to understand the relationship between the input and the output. I know that you can use the FFT to do pitch shifting, time stretching, equalization, and a bunch of other cool shiznat... that's what I'm interested in.
Posted by CaptainEO on Apr. 20 2002,04:15
Fourier analysis means expressing a signal as a sum of pure sine waves at various frequencies... e.g. "A bit of 1Hz sine, plus some 2Hz sine, and lots of 6Hz sine"... (in a very rough way, you can imagine "dividing" a function by various sine waves to determine how much of that frequency exists in the function). Any periodic signal can be broken down this way, altough you may need lots (up to an infinite number) of sine waves across a large range of frequencies to express it accurately. Fortunately lots of interesting signals are limited to a narrow band (e.g. audible sounds go roughly between 0Hz - 22kHz).Lots of image- and audio-processing techniques involve Fourier-analyzing a signal, mucking with the component sine waves in some way, and then reconstructing a modified signal by summing them up again. e.g. an audio equalizer works by enhancing or reducing certain frequency ranges by increasing or decreasing the amplitude of the component sines at different frequencies... a 2-D "blur" or "sharpen" filter for image processing works essentially the same way; it just emphasizes certain frequencies (low frequencies for blur, high frequencies for sharpen)... A frequency filter isn't strictly necessary to time-stretch audio, but you can get better results if you pre-filter the signal to eliminate frequencies that wouldn't be representable at the new rate.
However, if you look at the code for a real blur or sharpen filter, you probably won't see a Fourier transform... You'll see a N by N filter, where each pixel (or audio sample) is set to a weighted sum of its neighbors. The effect of a per-sample weighted sum is mathematically equivalent to a Fourier transform, then a per-frequency multiplication, then an inverse Fourier transform... And when writing fast filter code it often helps to take advantage of this property. (MMX, SSE, etc are all designed to accelerate operations like this)
Posted by Non on Apr. 21 2002,01:38
Huh? 
Posted by just_dave on Apr. 22 2002,21:08
| Quote (CaptainEO @ 19 April 2002,11:15) |
| Scientific Stuff Here..... |
What scares me if I accutally understand most of that, as in messing with sine waves and crap, it releates to filters in Audio, as in High Pass, Low Pass, Band Pass, and Band Stop... its stuff you learn in AC Electronics and crap but the Fourier or whatever the brak its called ... is unknownst to me..
dave