what´s the current state in fractal-audio compression?

[ReinerSchweinlin]

Hy there!

I was wondering if there is something similar to fractal image compression in the audio-world. A search in google provided a lot of hits, most of them stating that there is no usable peace of software out up to this point. See also:
http://www.halfbakery.com/idea/Fractal_20Audio
Does anybody know of some further development on this subject?

Greets Reiner Schweinlin

[General Lee D. Mented]

I don't think audio has much of a fractal structure. Fractals retain the same appearance when scaled and arbitrarily rotated. If you scale audio you're not going to get the same wave shape as you just saw, even if you shift it in phase or something.

What you'd need for audio is an adaptive-basis wavelet transform, where the system attemps a transform with a set of various base functions, finds the most compressable result, then encodes it and calculates the difference, then repeats for the difference waveform. Thus if it were really good you could transform using wavelets similar to the instrument base waveforms and each pass would be the coefficients of a different instrument.

In practiced this would probably be hard to write and take enormous cpu time.

[Neo Neko]

Originally posted by General Lee D. Mented
I don't think audio has much of a fractal structure. Fractals retain the same appearance when scaled and arbitrarily rotated.

Actually a fractal is a shape or pattern created by an infinantly repeating patterns. And it should be possible to do lossy encodes with fractles. One particlar point in which they would likely be usefull is in compressing harmonics. They can often display similar characteristics like fractles and are common throughout most music. So a fractle encode would only need to represent the first harmonic. And then replicate and scale it for the second and third etc.

Originally posted by General Lee D. Mented
If you scale audio you're not going to get the same wave shape as you just saw, even if you shift it in phase or something.

Actually when scaled propperly and viewed propperly the visual waveform would be identical. All that would change are frequency and amplitude.

[General Lee D. Mented]

Originally posted by Neo Neko
Actually a fractal is a shape or pattern created by an infinantly repeating patterns. And it should be possible to do lossy encodes with fractles. One particlar point in which they would likely be usefull is in compressing harmonics. They can often display similar characteristics like fractles and are common throughout most music. So a fractle encode would only need to represent the first harmonic. And then replicate and scale it for the second and third etc.

I know what a fractal is. Harmonics are fairly easy to generate if you want but how does that help with compression at all?



Actually when scaled propperly and viewed propperly the visual waveform would be identical. All that would change are frequency and amplitude.

That's just adjusting for variations in frequency and amplitude, it's not fractal scaling. a 100hz wave isn't made up of a series of 1000hz waves of the same shape, audio doesn't look like that. It doesn't have a fractal structure. You can't zoom in on a waveform and see the same waveform shape repeated at a higher frequency as a composition of the original waveform, it doesn't work like that.

[Neo Neko]

Originally posted by General Lee D. Mented
I know what a fractal is. Harmonics are fairly easy to generate if you want but how does that help with compression at all?

It should be possible to express an entire harmonic sequence as a fractal equation set.

Originally posted by General Lee D. Mented
That's just adjusting for variations in frequency and amplitude, it's not fractal scaling. a 100hz wave isn't made up of a series of 1000hz waves of the same shape, audio doesn't look like that.

Are you sure? I can think of several scenarios where a waveform could be made up of an infinant number of similar smaller wave forms. Well as infinant as the sampling would allow. :P

Originally posted by General Lee D. Mented
It doesn't have a fractal structure. You can't zoom in on a waveform and see the same waveform shape repeated at a higher frequency as a composition of the original waveform, it doesn't work like that.

Actually it does. You only think it does not because of the way in which each is viewed. A graphical fractal can be two or three dimensional. Either expressed in terms of X and Y or X, Y, and Z with no real restriction on the terms. An audio fractle would look different due to the nature of one of its axis. It is expressed in terms of T and Y axis with T being restricted to a strict linear progression. But that does not preclude the existance of an audio fractal. And the benefit of something like an audio fractal I think would be highly obvious. Technically infinite resolution in a finite equation. The compression savings in theory at least could be staggering. Though I suspect that much like the area of graphics and video it is going to be a while before it becomes that viable. Speaking of fractal compression does anyone still have the fiasco source or any binaries? Why not integrate it into ffmpeg and ffdshow since we are putting everything else in it. ;)

[General Lee D. Mented]

A fractal is a shape that's expressed recursively. I don't think audio is very recursive, at least not in most practical uses like music. It can be repetative, such as with chords and rhythms and that's compressible but not recursive, so not a fractal. The basic waves are cyclic hence why FFT is so suitable for it but again they're not recursively constructed. If you have a specific algorithm in mind or an example of a case where you could recursively compress audio with benefits please let me know, because I can't think of one.

[Manao]

Neo Neko : If I understand correctly what you said, you want to represent a waveform by a fractal equation set. But a fractal equation set in our case only gives one value, because the possibly fractal part of the audio signal has only one dimension. So I can't see how we could build a compression scheme out of that.

[Neo Neko]

Hey manao long time no see. ;)

I am not an audio or math expert. I just know enough to get myself in trouble. [ Just ask Dibrom :p ] But I have to ask as someone who has seen graphs of audio wave forms how could that be considdered one dimensional? Sure the waveform is represented by a one dimensional line. But it moves in two dimensions. Does it not? And I have seen fractal examples several times that produce errily similar patterns to audio wave forms. The only difference is that instead of unrestricted terms of X and Y you have an unrestricted term of Y and a restricted term of T.

Now I am not saying that it would be easy. But simply entertaining the possibility. The possibility that a smart encoder using additive fractal equations with linearly restricted terms of X or T is possible. Even if perhaps not that feesable yet.

[ReinerSchweinlin]

Hello there

Thanx for all yout posts, this cleared up things a bit. I guess, it´s too soon for such a thing as fractal Audio-Compression, but doesnt´s seem to be totaly impossible.

Greets Reiner

[General Lee D. Mented]

After doing a little research recently, I think people may be saying "fractal compression" when what they mean is "arithmetic coding". Arith coders use a fractal-like system where they divide a floating point range from 0 to 1 into N spaces, one for each symbol in the set. When a symbol is read, the output data is a value within the range of that symbol, the system updates a probability model based on the symbol read, and then the range is restricted to the min/max bound of that symbol's region. Then that smaller range is divided into N spaces, and the process repeats, like a fractal zoom on the 0-1 floating point space where the symbols determine which region to zoom into.

If you wanted to use this for audio, I assume it could be done with any arithmetic compressor like PPMZ or DMC but I doubt it'd do much because audio is cyclical and you'd need a system that "knows" about the data to exploit that. If you did something like say, find the peak of every wave in the waveform, then code their differential position and absolute height with two arithmetic streams (thus getting frequency/phase as one stream and amplitude as the other) you might get something. But you've lost all the interpolative data between the points, so you'll have to estimate it on decode with something like a spline generator or you'll get either square waves (bad) or sawtooth (if you use linear interpolation) which is also not good.

If anyone cares to work on this let me know and I'll see if I come up with anything clever, but right now I'm too busy with my own algorithms to write this thing up. :P