Re: [LAU] ambisonics and number of speakers

On Sun, Feb 28, 2010 at 12:03:50PM +0100, Jörn Nettingsmeier wrote:

> generally, it seems to be advisable not to use too many speakers for any
> given order. 8 is great for 3rd order horizontal, ok for 2nd and
> probably too many for first. there is a sound scientific explanation for
> this which i have forgotten... let me try (and i hope fons will jump in
> if i'm getting stuff badly wrong):

(/me jumps in)

> i believe it has to do with the blurring of the energy vector at HF -
> ideally, you want just one speaker to play a discrete source (which
> means rE equals one, for a source coming from where the speaker is).
> the higher the number of speakers that contribute (and if your signal is
> first order, all speakers will, to some extent), the lower the energy
> vector, which means you only get good directional cues in the LF band.

No this is not true, the rE does not decrease when you use
more speakers.

The effect can be understood in terms of spatial sampling
and aliasing.

To reproduce the field of a real source, you need *all*
spatial harmonics, in theory (for a real point source)
up to infinite order. So An AMB system of order N must
not just recreate the harmonics up to order N, but *all*
of them. It will control some of them (but no more than
the number of speakers), and the rest has to be generated
by aliasing.

A first order horizontal decoder with 4 speakers will
exactly control the levels of the 0, 1st and 2nd order
components, and the rest is filled in by spatial aliasing.
The aliased components are not exact of course, and that's
why localisation will be impaired if you move away from
the sweet spot.

Now if you use e.g. 8 speakers to reproduce horizontal first
order the system controls components up to 4th order. If the
input is just first order, the 2nd and 3rd order components
will be zero, as will be all those that alias from them (5,6,
10,11,13,14, etc.) The result is a field that does not match
well to that of a real source.

Ciao,

-- 
FA
O tu, che porte, correndo si ?
E guerra e morte !
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