if you could do an infinite-size FFT

... what would the spectrum analyzer look like for it, or start to look like with the right sounds? Would it just go on and on like a fractal or what. Melda Manalyzer allows for 262144 point analysis and it started to look a little hypnotic and weird and you could keep zooming in for quite a while before you reached the smallest sound pixel or whatever you want to call it. I know SINE WAVE would be a single point ideally but what about sawtooths/square waves/white noise and whatever kinds of distortion

 

edit: also assume sampling rates could also go to whatever ridiculous extreme you want it to

Edited December 18, 2013 by Ragnar

plenty of interesting directions to take a discussion about fft but i don't think there's anything too groovy going on visually. your butting heads with too many different software drivers and hardware parts to have a reasonable hypothetical train of thought like this.

  On 12/18/2013 at 9:06 PM, RadarJammer said:

plenty of interesting directions to take a discussion about fft but i don't think there's anything too groovy going on visually. your butting heads with too many different software drivers and hardware parts to have a reasonable hypothetical train of thought like this.

 

>:(

Frequency resolution trades off against time/temporal resolution. Food for thought.

is that like the heisenberg uncertainty

Would it go on like a fractal?

 

What is smallest possible difference in frequency? That's a weird question - if you had two frequencies very slightly different together - they would cancel out over time right? So since all frequencies are bound together and interact in this way... arrggghh my brain

Doesn't everything just break down to sine waves at a macroscopic level ? So everything would just become various width wobbly lines I reckon

  On 12/19/2013 at 1:53 PM, mcbpete said:

Doesn't everything just break down to sine waves at a macroscopic level ?

Ommmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

  On 12/19/2013 at 1:53 PM, mcbpete said:

Doesn't everything just break down to sine waves at a macroscopic level ? So everything would just become various width wobbly lines I reckon

Actually scrap that - got my spectral and waveform views mixed up regarding sine waves. I reckon it'd be a point cloud of partials

The Fourier transform is essentially an "infinite sample rate FFT" if you want to think it like that. It's over the whole continuous real or complex number domain. It transforms a given real or complex function from a "time domain" to a complex "frequency domain". It's usually solved algebraically by solving the integral of the given time domain function. The problem is that it might really hard or impossible to solve into any decent form. This goes very deeply into complex and functional analysis (functions as vectors etc.).

 

FFT is just a discrete version of the Fourier transform that can be calculated to any given finite set of discrete samples in time domain.

 

So anyway, for an example, if you take a continuous rectangular function like this in time domain:

Do the hocus pocus with the integrals and transform it to frequency domain, you will get a sinc function like this:

 

</math nerd>

 

 

 

Nah it's really interesting. I'm currently working though this book -

 

 

And it's kind of blowing my brain at all the things I've taken for granted as standard audio effects/techniques without having a slightst clue of the theory behind it all

Yeah, I find it interesting too. It's actually pretty mind blowing. What the Fourier transform does is that it maps the time domain function into an infinite (actually uncountably infinite) dimensional vector space where the trigonometric functions sin and cos in different frequencies are the basis vectors.

 

Shit like this is why I love mathematics.

they say you can recreate all sounds with sine waves, but ive never heard it done

sine waves within sine waves.

 

essentially, the universe is made of wobbly brostep.

  On 12/21/2013 at 6:01 PM, marf said:

they say you can recreate all sounds with sine waves, but ive never heard it done

Technically you have - When your speaker oscillates backwards and forwards it's doing sine wave approximations of the orinigal sound

It's just mathematics, every integrable function can be represented as an integral (=infinite sum) of sines. Sound as a finite energy signal is integrable. You can use other periodic and non-periodic functions as well if you want, sines are just the most common and natural.

  On 12/21/2013 at 6:10 PM, mcbpete said:

 

  On 12/21/2013 at 6:01 PM, marf said:

they say you can recreate all sounds with sine waves, but ive never heard it done

Technically you have - When your speaker oscillates backwards and forwards it's doing sine wave approximations of the orinigal sound

 

 

thats mind blowing. you are right. what is the fault of software in this regard?

magnets.

  On 12/21/2013 at 7:40 PM, phling said:

magnets.

fft is the music equiv of doing shrooms. using just a pinch of FFT is a big statement in your music i think. if your not careful its got that elastiq pro wheres waldo effect to it where if there is a full mix your mind will naturally wander over to the one fft noise in the background and try and pick at it because the signal type doesn't follow the same common sense as the rest of the sound palate.

  On 12/19/2013 at 12:17 PM, futureimage said:

Frequency resolution trades off against time/temporal resolution. Food for thought.