On Wed, Mar 27, 2019 at 04:50:06AM +0800, Stephen McArdle wrote:

> I think the question might be more simpler than this.
> For 1st order (with 4 microphones) the very first A to B
> equations are (for example):

> W' = FLU+FRD+BLD+BRU
> X' = FLU+FRD-BLD-BRU
> Y' = FLU-FRD+BLD-BRU
> Z' = FLU-FRD-BLD+BRU

It's not that simple. This would work if

* your capsules are exactly hypercaridiod (i.e. max
  directivity), independent of frequency, and
* they are *perfectly* matched.

That is not the case in practice. Even if the capsules
are high quality and well matched you will need some
EQ in addition to these simple sums.

> What would the equations be for 8 microphones?
> W' = FLU+FRD+BLD+BRU+FRU+FLD+BLU+BRD
> X' = FLU+FRU+FRD+FLD-BLD-BRU-BLU-BRD
> Y' = FLU+FLD+BLD+BLU-FRU-FRD-BRD-BRU
> Z' = FLU+BRU+FRU+BLU-FLD-BLD-FRD-BRD

No, this is completely wrong, ignores all practical
aspects, and again it's not that simple.

> But what about R’,S’,T’,U’ ??

Much more complex again.

In practice you can't do this to sufficient accuracy
without rather complex EQ or convolution.

And anyway, trying to do A/B conversion (or even Ambisonic
decoding) in environments like PureData, SuperCollider and
similar is a sure recipe for disaster. These are all
*artistic* tools, and they don't allow for the precise
technical definition of e.g. the required EQ. Apart from
that the probabily of making some simple but fatal error
is way too high for a reliable result.

Ciao,

-- 
FA

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