On Mon, Feb 28, 2022 at 10:05:53PM +0200, Sampo Syreeni wrote:

A lot of jargon without much real meaning, at least not as far
as my limited brain powers are able to detect.

> In particular, nobody's been bold enough yet to implement zero delay
> provably constant effort convolutions of the Gardner/Lake DSP kind, so that
> the library doesn't have to be thought about, as a component.

General purpose libraries doing efficient zero delay convolution using
multiple partition sizes (as suggested by Gardner) do exists. But they
are complete overkill for the simple problem at hand (decoding UHJ).
Even the most basic FFT-based implentation wouldn't take more than one
percent CPU time on a ten year old PC or something like a Raspberry Pi.
 
> One of the things I've been wondering about for the longest time then is how
> to optimally, actively decode a B-format signal. How to do what I think
> Angelo Farina at one time called "an infinite order decode".

Some people think they can build a perpetuum mobile. Or extract
information out of nothing. Or think they can trick others into
believing such things - which may be true.

For each finite-order B-format, there are wildly different source 
distributions that will produce exactly the same B-format signals.
It's quite easy to generate signals that will produce a completely
wrong output from Harpex or similar systems.

So any parameteric (assuming that is what you call 'active') decoder
will have to start with some assumptions which may be wrong and will
be wrong at least part of the time.

Also the distinction plane wave vs. diffuse is a bit too simple.
Consider a choir (say 30 singers) distributed over a 90 degree horizontal
arc, singing unisono. If you want to decode this as 30 point sources
you'll need very high order. But it's not diffuse either. It's something
in between, and a good parametric decoder should be able to detect such
source distributions.  

In practice such things become possible in practice if you start with
something like third or higher order. But the maths are by no means
trivial. And if you have third or higher order, a corret linear decode
will provide very good results and there is little reason to go parametric.
 
> I believe the principled way to go about this would be to treat the field as
> complex, and harmonic, then to square it in order to find point sources,
> express that instantaneous solution as a higher order complex spherical
> harmonical expansion, extract the out-of-phase component for DirAC-like
> processing, and to apply some time-running polynomial of the adjugate of the
> system function to set a variable time-frequency tradeoff.

Does anyone have a clue what this is supposed to mean ?

> Actually you *do* need Z. That's the point where I alluded to Christoph
> Faller above: if you cut out the third dimension, your reconstructed field
> will show a 1/r extra attenuation term from the rig inwards, because you're
> bleeding off energy to the third dimension.

You need the third dimension for realism. Not for correct decoding.  


Ciao,

-- 
FA

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