fourier question

so I'm reading this book on quantum mechanics and it gets to talking about the fourier transform. I knew any wave could be broken down into sine waves, but I didn't know what it said after that, which is that you can also break down any wave into waves of any other shape - like, you could add up square waves or piano samples to make a sine wave if you had them at the right pitch, amplitude and phase. that's crazy! is there any software where you can do this? like, load up a sample, load up another sample with a cycle of a waveform, and decompose the first one into a bunch of waves based on the second?

matlab?

Welcome to the Fast Fourier Transformation (fft), today any dsp use this theory to get the spectrum and processing. You use it all the time and you didn't know :)

i think he was talking about the non-(co)sine transformation, i don't think that's even called fourier transformation...

  Quote

i think he was talking about the non-(co)sine transformation, i don't think that's even called fourier transformation...

transforms like the haar transform (using wavelets), walsh transform (orthogonal squarewaves) and the hadamard transform use the same principle of orthogonal superposition & decomposition as the fourier transform, they are however not as common in sound processing as the fourier transform because the fourier transform always presumes harmonic (sinusoidal) vibration/oscillation in a system, instead of the two-state (or, in the case of wavelets, non-periodic) oscillation in certain mechanical and quantum-related systems.

numerical analysis software like matlab, maple, etc, can all do these transforms, most of them in real time (since they all have "fast" versions like fourier transform's fft). you'll have to mess around a bit with your input signals, and the way you'll plot the decomposition, but there's plenty of examples floating around (these kinds of non-harmonic transforms are pretty common in non-sound dsp).

edit: walsh transform, not welsh transform (that would've been cymreig trawsffurfi or something)

I think I need to go back and finish college with better calc teachers and sleep habits before I can do this... was hoping there was already something like mammut for this kind of thing. but thanks.

welsh transform lol.

I study electronic engineering. Halfway through third year just finished a course in signals and systems. Basically the foundations of this signal processing. MAD. MAD .

Defining signals in terms of either continuous or discrete time and then using calculus to process them. Check the notes for the course. I've got a few MATLAB codes we had to write in labs but I don't know if you have the software to run them.

Signals And Systems

  pera said:

Welcome to the Fast Fourier Transformation (fft), today any dsp use this theory to get the spectrum and processing. You use it all the time and you didn't know :)

so that's why squarepusher mentions "FFT" in his rap (do you know teh squarpasher?), alongside "DSP"....it all makes sense now!

I don't think I would even go so far as to say most dsp(in regards to audio) uses fourier transforms much the less any.

  Bubba69 said:

I don't think I would even go so far as to say most dsp(in regards to audio) uses fourier transforms much the less any.

NI Spektral Delay

  Bubba69 said:

I don't think I would even go so far as to say most dsp(in regards to audio) uses fourier transforms much the less any.

eq, filter, reverb, "advance" delay, "advance" distortion, additive synthesis... etc etc use fft :)

how does reverb use fft, is it for smoothing/blurring things out? you can also make reverb just with delays or allpass filters.

multiply the fft of one sound with the fft of an impulse response of a acoustic space: (convolution) reverb

oh yeah, forgot about that.

  spraaaa said:

how does reverb use fft, is it for smoothing/blurring things out? you can also make reverb just with delays or allpass filters.

MANY allpass filters :D

this thread is about final fantasy tactic right?

^ the welsh version, yeah

very small number of allpass filters + an env controlling delay time doesn't sound like reverb, but it's tight

what do you mean delay time... the filter delay depends on filter topology, but i don't know of any analogue filter type where you can vary the delay

or do you have an actual delay module in there too, in which case - why the allpass filters?

  kokoon said:

what do you mean delay time... the filter delay depends on filter topology, but i don't know of any analogue filter type where you can vary the delay

 

or do you have an actual delay module in there too, in which case - why the allpass filters?

the delay in an all-pass filter is a phase shift. check out lattice filters, they are what analog all-passes often look like (bridge-style topology), tie a bunch of them together, use some shunt resistors/potentiometers to mess with the inductance and there you have it, real-time phase shifting :)

the phase shift is frequency-dependent so you can use it to simulate the fast reflection of high freqs and the slower reflection of low freqs in a space.

early forms of electronic reverb, are almost all simple all-pass (plus comb) filter networks, not even using that many all-passes. a variety that was used a lot in the early 80s by lexicon, yamaha etc was the schroeder reverb & its offspring: a few parallel comb filters, summed, and fed thru a few sequential all-pass filters (i think the original schroeder version used just three all-pass filters), like this:

the idea is that the combs give a (very crude) diffraction (simulating what frequencies get filtered out when the sound hits the walls) and that the all-passes do frequency-dependent delay (diffusion, and size of the space/length of the delay). try it out, it's crude (tinny, typical comb sound) but can sound cool.. especially if you add more filters and start messing and modulating around with their settings :)

googling around on various points in this thread, i stumbled upon a paper entitled How I lost 150 lbs. thanks to Max/MSP

Yeah i'm curious about this myself, i think audiosculpt from ircam is supposed to be the best for this sort of thing. Only for osx unfortunately.

^ (edit - this is pointing thru jim's post to that link but hey audiosculpt looks cool but way expensive) interesting, working on the same kind of thing right now, except without starting with hardware

  iep said:

  kokoon said:

what do you mean delay time... the filter delay depends on filter topology, but i don't know of any analogue filter type where you can vary the delay

 

or do you have an actual delay module in there too, in which case - why the allpass filters?

 

 

 

yeah, this is exactly what I had, found a diagram of the shroeder reverb in a library book on electronic music from the 70s. when setting it up in plogue bidule, each filter has one input for signal and one for delay time, so I added a variable to multiply all the time values before they went in. it sounded cooler changing than at any one setting so then I added an envelope to do that.

  spraaaa said:

^ (edit - this is pointing thru jim's post to that link but hey audiosculpt looks cool but way expensive) interesting, working on the same kind of thing right now, except without starting with hardware

 

  iep said:

  kokoon said:

what do you mean delay time... the filter delay depends on filter topology, but i don't know of any analogue filter type where you can vary the delay

 

or do you have an actual delay module in there too, in which case - why the allpass filters?

 

 

 

 

yeah, this is exactly what I had, found a diagram of the shroeder reverb in a library book on electronic music from the 70s. when setting it up in plogue bidule, each filter has one input for signal and one for delay time, so I added a variable to multiply all the time values before they went in. it sounded cooler changing than at any one setting so then I added an envelope to do that.

ah, i see. though that's impossible to make in analogue realm, the filters have a frequency-dependent, fixed delay time (true, "phase shift").

  spraaaa said:

not exactly what i was looking for but not not awesome enough not to link

just got into this program myself, its great for FFt messing around.

anybody here ever mess with FFt in max/msp ? Some french dude i forgot his name made a bunch of Jitter patches designed to read the audio of a wave form then convert its FFT/spectral print to a video or still image. Then you can manipulate this still image with video effects like blur, distort, pixelate. Its pretty awesome, its probably the most interesting way to manipulate FFT's visually besides Metasynth and Spear

i regularly check probably twice a month to see if the dudes who made Scambledhackz have released their source code yet. Unfortunately i dont think they have but if they did this would open up huge possibilities for music making. If you subtract the video element from this technique and just imagined what loading up a bunch of sounds and creating a spectral/fft database of each one and creating an algorithm to 'match' them up with the most mathematically similar sound would be freaking amazing.

does anybody know if something similar to this FFT database compiler exists for use? it makes me wonder if this dude just made this for a hobby or if he's looking for buyers of this code. It's been over 4 years since he did this and i haven't seen this concept commercialized yet. I could see a ton of practical and professional uses for this technique