> Hey...not a amthmetician. But, i like math.
>
> I got Trig, Calc, and other shit under my belt. So, if I can help...I'd be
> glad.
Hm, I should know better than to be vague.
*Specifically* I'd be looking for someone intimately familiar with direct form
II IIR filters, the Levinson-Durbin and Schur algorithms for producing
coefficient sets and the underlying linear and discrete math.
The fundamental difficulty with lossless compression techniques that make use
of LPC is that nearly all the energy is concentrated into very narrow features
in the the low frequency spectrum. LPC filters of a given order generally are
able to reproduce roughly equal-width features (this is a generalization) on
the order of the size of the spectrum evenly split into bands by the order of
the filter. Representing the LPC filter in LSP form makes this very plain
(look at the frequency peaks and where the LSP coefficients appear by mapping
the first half of the unit cirlce to the spectrum). A classic LPC filter
approximates all of the narrow low frequency features with a single very
roughly fit formant-like curve.
LPC filter generators will try to match wide features first, and so blow all
their resolution of the high frequencies which are mostly noise, and ignore
real peaks in the first few octaves (due to the log nature of octaves, these
features are very narrow). If we could come up with an LPC filter mechanism
that makes use of spectral features with widths naturally based on the octave
they appear in, 4:1 lossless should not be too difficult to acheive.
I'm not aware of any LPC filer mechanism that can do this. The closest I've
come is in Vorbis: I map the linear frequency scale to a log scale and do my
LPC-based frequency spectrum encoding there. Vorbis's LPC thus sees peaks
nicely, but it's an approximation acceptible for a lossy compression, not
acceptible for lossless.
Thus, to use the log-frequency-scale LPC filters, we need to invent some math
(and undoubtedly come up with a slightly different set of constraints as a
classic direct IIR filter with log-scale-width frequency features is likely not
possible).
Monty
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