[opus] Fwd: [EXT] Re: Coarse energy predictor confusion

[Jake Taylor]

Apologies, I forgot to "reply all".

---------- Forwarded message ---------
From: Jake Taylor <yupferris at gmail.com>
Date: Mon, Jul 5, 2021 at 9:29 AM
Subject: Re: [EXT] Re: [opus] Coarse energy predictor confusion
To: Ulrich Windl <Ulrich.Windl at rz.uni-regensburg.de>


> Personally I think your thoughts could be valuable to people trying to
understand the code.

I was planning to blog about this, basically repeat the last notes and add
some stuff about going the other way (eg. swapping terms so that the
decoder can work without knowing the current energy value yet, and then
deriving the code). I suppose it could be useful to share a link to that
when it's ready?

On Mon, Jul 5, 2021 at 9:26 AM Ulrich Windl <
Ulrich.Windl at rz.uni-regensburg.de> wrote:

> >>> Jake Taylor <yupferris at gmail.com> schrieb am 03.07.2021 um 13:51 in
> Nachricht
> <CALkcPkLpPT1kG5KLpQ4ZHoTYRHJukNH58=ThYCJF-m7kZRV9Xw at mail.gmail.com>:
> > Hi again all,
> >
> > I've solved it (in fact the clues showed up in earlier notes, but I
> didn't
> > put it together entirely until now)! I was making a crucial conceptual
> > mistake. I assumed the output of the predictor was the *prediction*,
> > however, this is incorrect - instead it outputs the *residual* directly.
> > Under that interpretation, everything falls into place. So I no longer
> need
> > help with this, and sorry for the noise while I figured it out!
>
> Personally I think your thoughts could be valuable to people trying to
> understand the code.
> Maybe it could be "weaved in" or added to the resources at the web site.
>
> >
> > For the curious, once again, notes in pdf/lyx format are attached, as
> well
> > as on my dropbox:
> > pdf:
> > https://www.dropbox.com/s/rzm08055hytjy6c/predictor-confusion-5.pdf?dl=0
> > <
> https://www.dropbox.com/s/l4tzyvq1mne8jan/predictor-confusion-4.pdf?dl=0>
> > lyx:
> > https://www.dropbox.com/s/vj1s3pbm8q914vf/predictor-confusion-5.lyx?dl=0
> > <
> https://www.dropbox.com/s/map3slkbnhyctui/predictor-confusion-4.lyx?dl=0>
> > and plaintext below.
> >
> > Thanks again,
> > Jake
> >
> > ---
> >
> > Opus Coarse Energy Predictor Notes (Round 5)
> >
> > Jake Taylor (yupferris at gmail.com), 3 July 2021
> >
> > I've solved it - I was simply mistaken about what the output of
> > the filters should be. Instead of the filters outputting the
> > prediction, they output the residual directly. Under this
> > interpretation, everything falls into place.
> >
> > According to the paper[0]/RFC[1], the 2D z-transform should be:
> >
> > A(z_{\ell},z_{b})=(1-\alpha
> z_{\ell}^{-1})\cdot\frac{1-z_{b}^{-1}}{1-\beta
> > z_{b}^{-1}}
> >
> > I've simplified the source code (in unquant_coarse_energy in
> > quant_bands.c in libopus 1.3.1[2]) to the following C (pseudo)code:
> >
> > void unquant_coarse_energy(float *e, int bands) {
> >   float alpha = /* ... */;
> >   float beta = /* ... */;
> >   float prev = 0.0f;
> >   for (int b = 0; b < bands; b++) {
> >     float r = /* read from bitstream */;
> >     e[i] = alpha * e[i] + prev + r;
> >     prev = prev + (1 - beta) * r;
> >   }
> > }
> >
> > The goal is simple: extract difference equations from the code,
> > derive the corresponding z-transforms, and then solve the final z
> > -transform which should hopefully match what the paper/RFC list.
> >
> > The code is governed by the following difference equations:
> >
> > e[\ell,b]=\alpha e[\ell-1,b]+prev[\ell,b-1]+r[\ell,b]
> >
> > prev[\ell,b]=prev[\ell,b-1]+(1-\beta)r[\ell,b]
> >
> > The corresponding z-transforms are:
> >
> > E(z_{\ell},z_{b})=\alpha
> >
> z_{\ell}^{-1}E(z_{\ell},z_{b})+z_{b}^{-1}Prev(z_{\ell},z_{b})+R(z_{\ell},z_{
> > b})
> >
> >
> Prev(z_{\ell},z_{b})=z_{b}^{-1}Prev(z_{\ell},z_{b})+(1-\beta)R(z_{\ell},z_{b\par
> >
>
>
>
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