Algebraic (or Vector) Sampling - does it exist?

bizack · Post by **bizack** » Wed Dec 28, 2005 3:48 am

That's not a true statement. You can physically model anything. It's most often used in audio applications to model acoustic instruments. But you can also model bouncing balls, particle systems, etc.

But yeah, I think he's looking for something else anyway.

Perhaps his idea is similar to vector fonts in the graphics world, but applied to audio.

sweetjesus wrote:
bizack wrote:Isn't this what Physical Modeling does, to some degree? Also, Waveguides and Wavelets.
physical modelling is when you try and recreate circuits using code.

he wants resynthesis..

check out the Hartmann Neuron. If you can still get it, thats what this does.

here's whole bunch of other stuff that will also do what you need
http://www.kvraudio.com/news/1482.html
http://www.sonicstate.com/news/shownews.cfm?newsid=1679
http://www.concretefx.com/Kubik.htm
http://www.discodsp.com/vertigo/

M. Bréqs · Post by **M. Bréqs** » Wed Dec 28, 2005 7:01 am

SimonPHC wrote:The problem Exists when you have to translate you formulae back to a list of samples. You'll always have to do this! You work the formulae out, set a sample rate at which you poll results for a certain x give y ... but digital devices will always use some kind of clock, rate, frequency, lalala what ever you call it. the vectors won't matter in the end. It's not graphic stuff...

I was originally going to rebuke your post, but after consideration I realise that you're right!

If your CPU cycles at 3GHz (a reasonable ammount today) then even with vector sampling, you'll still be taking a max 3 billion samples per second of your wave form... And that's even assuming that you can get audio out of your machine with only 1 process per CPU cycle (a technological impossiblity).

So, really all you're doing is just introducing a new storage media, since it's going to be cut up into samples anyways.

M. Bréqs · Post by **M. Bréqs** » Wed Dec 28, 2005 7:05 am

I wasn't really asking about physical modelling, though the principals would be the same. I'm talking about physical modelling in reverse I suppose. You would record an infinitely indivisible wave of audio into a computer and record the actual formula of the resultant wave. With physical modelling, you create a stepped wave by applying a formula (2 x Sin for instance for a sine wave) that is then output at a certain sample rate.

For resynthesis, like the Hartmann Neuron, I don't even begin to understand what that thing does - nor why it's so expensive!

By the way all - thanks for the discussion, I really enjoy this. I'm not trying to come off like a smarty pants, but I was realy wondering if it was possible...

Again, props to all respondants! This is why I dig the Ableton Forums!

bizack · Post by **bizack** » Wed Dec 28, 2005 7:24 am

Well, I guess you could explore Genetic Algorithms. You could use Genetic Algorithms to learn what function produced the waveform you're hearing as audio. GAs are used quite often to learn complex mathematical functions. I briefly looked at the Hartmann Neuron, and I believe they're using some AI techniques for resynthesis. There's a lot of research in that field. Do a search for Neural Networks + Self Organizing Maps + Genetic Algorithms + Music + Sound Synthesis.

M. Bréqs wrote:I wasn't really asking about physical modelling, though the principals would be the same. I'm talking about physical modelling in reverse I suppose. You would record an infinitely indivisible wave of audio into a computer and record the actual formula of the resultant wave. With physical modelling, you create a stepped wave by applying a formula (2 x Sin for instance for a sine wave) that is then output at a certain sample rate.

For resynthesis, like the Hartmann Neuron, I don't even begin to understand what that thing does - nor why it's so expensive!

By the way all - thanks for the discussion, I really enjoy this. I'm not trying to come off like a smarty pants, but I was realy wondering if it was possible...

Again, props to all respondants! This is why I dig the Ableton Forums!

conny · Post by **conny** » Wed Dec 28, 2005 1:00 pm

Interesting. Reminds me of a picture compression method called fractal compression or something like that. Guess it looks for patterns and repeated patterns and formulas that describe the patterns and their modulations...

If an image is just one clear red square on white, the "vectors" are quite obvious and the formula for recreating it is very small compared to the number of pixels.

Information theory?
A musical/sound DNA?

If the sound is very complex, the description ("vectors") will have to use as much data as the sound itself. (?) A single sine would not need more then a couple of vector instructions, though.

Basicly: Creating an abstract "language" to represent a sound. Analysis - abstract storage - resynthesis.
All three levels are creative in the sense of how to interprete the data.

// C

Kodama · Post by **Kodama** » Thu Dec 29, 2005 4:42 pm

Many Physical modelling synths are usually just comb filters and noise with control.

Most (all?) Resynths are usually just additive sine "partials" that are set to levels to mimic the original sound.

Physical mods can be interesting, but additives just sound like poor/dull time stretch samplers to me...

dirtystudios · Post by **dirtystudios** » Thu Dec 29, 2005 6:01 pm

I think it's brilliant. It would be the first time since vinyl that we would have an actual and accurate representaion of a waveform.

Well done.

k

M. Bréqs · Post by **M. Bréqs** » Fri Dec 30, 2005 4:44 am

dirtystudios wrote:I think it's brilliant. It would be the first time since vinyl that we would have an actual and accurate representaion of a waveform.

Well done.

k

Thanks. Though I agree that at this point, it's WAAAY too implausable considering the size of files you would need, and the complexity of calculating thousands of algebraic formulae at nearly the same speed that high end computers try to interpret a simple 24 bit number.

Think about trying to record 16 tracks at the same time like this! That's a very modest project, but would break even the best computers available today.

conny · Post by **conny** » Fri Dec 30, 2005 1:39 pm

I still think about it. The theory at least.
There are this balance between real data (sound) and instructions ("vectors", abstract descriptors).
When the latter gets more, it has to be more calculations in the end for re-producing the sound. Transfer through the net etc will be better but the load on the client will get higher?
In some sense this exists on rudamentary levels like transfering a midi program number (organ...) and some midi notes to client side reproduction.
But: Instead of analyzing and compressing a sound (mp3) we would like a analysis and "expressions" stage...
Perhaps interpolation between abstract patterns could recreate a sound?
// C

mosca · Post by **mosca** » Fri Dec 30, 2005 1:47 pm

*head explodes*

griper · Post by **griper** » Sat Dec 31, 2005 4:28 am

well, there's always a resolution... that's digital for you. the closer you got to the actual waveform, the more complex the waveform would get... only encoding/decoding would be much more intensive.

also, i have a feeling our ears are much more adept at picking out the simplicity of a waveform than picking out the number of samples

still an interesting thought, though i doubt it's efficient (processing required to create sufficiently accurate function vs just adding samples) enough

more interesting would be to take a standard file represented by samples and interpolate a truer waveform from the data... still don't know how analog you'd get considering all the steps between cpu and speaker

leonard · Post by **leonard** » Sat Dec 31, 2005 5:24 am

http://www.qubit.org/library/intros/comp/comp.html

conny · Post by **conny** » Sat Dec 31, 2005 1:24 pm

griper wrote: more interesting would be to take a standard file represented by samples and interpolate a truer waveform from the data... still don't know how analog you'd get considering all the steps between cpu and speaker

I'm not advocating the vector sampling as a storage or compression format. In my mind it would be much more fun to use the abstractions of a sound to manipulate them and then recreate it. Like for instance Cameleon, but for longer sounds and real time analysis - modification - recreation.

If it was a picture, you could use rules like "every round object will be rectangular and blue"...

// C

hambone1 · Post by **hambone1** » Sat Dec 31, 2005 1:48 pm

M. - you need to get out more... or go visit Conny...

M. Bréqs · Post by **M. Bréqs** » Sat Dec 31, 2005 11:04 pm

Hmmm.

Just stopped in to the forum before going out on New Years Eve, and what can I say - that link from leonard looks like quite the read. I'll have to get to that tomorrow.

Scratch that - the day after tomorrow. Hambone1, I'm gonan take your advice and go out! I'll be getting drunk tonight so I should be good n' hung over on New Year's Day.

That all said;

It might be possible to do a hybrid of this tech as griper suggested and use formulae to calculate the slope based on the rate of change between two samples in a standard digital audio format. However, I imagine that our ears do that anyways (or rather our brains). Since humans have a natural high frequency low pass filter, we would "round out" the jagged edges between the stepped differences of digitally sampled waveforms. Thus, using this on audio for human consumption becomes redundant, considering our ears do it for us anyways... No?

Really, what it all boils down to is that while vector recording is possible, there's no point: storage size is probably larger (for high freq sounds), as would be the processing drain, for an imperceptible gain in audio wave accuracy.

So, in my opinion, it's overkill for audio. You would probably need one modern, badass wikkid high end 64 bit gaming PC to do one single stereo track of audio, and then who knows what the latency would be considering the requirement to do lots of formulaic calculations?

The only way this is feasible is by replacing the very high freqs (at the limit of human hearing) with randomized white noise (with the low end filtered out). Why replicate randomness accurately when it's just random? If one could implement this, then it might be worthwhile from a listening perspective, but it's missing the point - now you're not truely recording audio, you're recording only a certain bandwidth and replacing the top end with randomness. While a human might not notice, a dog would.

HOWEVER:

Algebraic / vector recording probably has applications in SETI or electronic warfare (EW), looking for megahigh frequency patterns in radio waves. I am sure that if somebody's out there broadcasting intelligent patterns at a frequency higher than our digital storage media's resolution, we're missing everything.