How to Fourier Transform?

So how does one break a windows wav file into the component sine waves, together with phase and amplitude? People say one has to use DFT, but wikipedia article on DFT contains just some opaque formula, containing e with a complex superscript. How can it be used to produce C/C++-compilar uint32_t array of sine-wave frequencies? C/C++'s exp() cant even exponentiate e to a complex number.

And C99 doesn't support complex numbers at all.

You have to get a DSP chip in order to do it.

You can implement a complex exponential in three lines, why do you want to write a DFT yourself if you don't know the basics of complex numbers?

>>4

You can implement a complex exponential in three lines

That is a bad excuse for library functions to not support complex numbers.

why do you want to write a DFT yourself if you don't know the basics of complex numbers?

To learn how stuff works of course. Same way writing your own OS is the best way to learn how operating systems work.

>>5
You won't understand the mathematics behind the Fourier transform just because you badly translated an opaque formula to C. Similarly, the only thing you will get if you make an OS from scratch without any prior knowledge is a badly written OS. It's a godawful way to learn, and if you think about it this should be obvious: You deliberately ignored everything the people before you painfully figured out over decades.

If you want to learn how to make an OS, read a simple OS like Xv6.
If you want to learn how Fourier transforms work, get a book on complex analysis.
If you want to fuck around with sound files, just use a library that implements the transform for you; every major numerics library should have one.

>>6
Actually, making something from scratch with basic knowledge is a good way to learn. But yeah, it will be badly written.

>>7
Sure, if you have sufficient knowledge to begin with. OP would be better off starting with Matlab or IDL until they can at least grasp wtf is going on.

>>6

only thing you will get if you make an OS from scratch without any prior knowledge is a badly written OS.

Now tell that to Linus Torvalds.

C source code for DFT and FFT: http://paulbourke.net/miscellaneous/dft/

He also has an article on using fourier transform for video game terrain generation: http://paulbourke.net/fractals/noise/

>>9
Linux is pretty bad compared to BSD or Plan 9. The only thing it has over these two is a collection of drivers, which isn't an accomplishment of the OS. Linux is very messy and ad hoc, which is typical for things that grow out of hobby projects.

>>11

Linux is pretty bad compared to BSD or Plan 9.

Then why everyone is using Linux?

>>12
Features like accessibility, ease-of-use and software ecosystems make systems popular, not their internals.

>>12
Because that's where the drivers are, good luck getting a graphics card from this decade to run under Plan 9. Linux distros have also been going the Windows way for years, which sucks for competent users but increases user count.

>>14
New hardware doesn't have any standards. This was already a problem for sound cards in the 90s. If the architecture was cleaner, OSes would be much smaller and easier to create. Today's web scripts are more complicated than 80s operating systems.

https://en.wikipedia.org/wiki/WAV

https://en.wikipedia.org/wiki/Pulse-code_modulation#Modulation

https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Code_example

>>17
That is not fourier transform.

>>18
Nor is it a credible information source.

>>18
Fourier is obsolete.
https://georgemdallas.wordpress.com/2014/05/14/wavelets-4-dummies-signal-processing-fourier-transforms-and-heisenberg/

It still seems a bit over-complicated

Couldn't you run a few layers of smoothing / residual type thingos in realtime?


function wave(freq, phas, amp, t)
phas2 = (phas*2*pi) / freq;
w = amp .* sin(freq .* (t .+ phas2));
return(w);
end;


>>21
You could but since convolution in the time domain is equivalent to multiplication in the frequency domain, it's actually often less computationally intensive to go the FFT->filter->IFFT route for realtime processing.

bbbaa99887665543322111100000001112233445667889aabbcccddddddddddcccbbaa9988
87766555444443333334444445555666677777888888888888888888888887777777766666
6666666666666667777788889999aaaaaaaaaaaaaaa9998877665

4bit 100Hz of three tones (probably inaudible 7-13hz)

https://developer.mozilla.org/en-US/docs/Web/API/AudioContext/createBuffer

>>22

.*
.+

is that ML?