Re: [LAU] ambisonics and number of speakers

On Sun, Feb 28, 2010 at 02:21:08PM +0100, Jörn Nettingsmeier wrote:

> hmm. i still don't see from this explanation why 1st order horizontal
> sounds worse over 8 speakers (or 12, for the sake of argument) than over
> just six, even if i'm in the sweet spot.

Have a look at the Bessel functions (either spherical
or cylindrical, they are different but similar).

The degree N Bessel function determines how much an
order N component contributes to the pressure field,
in function of distance from the reference point
(= the sweet spot).
The argument is 2 * pi * distance / wavelenght.

With some imagination you'll see that for each
distance their is a set of orders that dominate
the reconstruction. If these harmonics are missing
then field reconstruction at that distance will
be impaired.

As an extreme case, just imagine that all harmonics
except the zero and first order ones are absent, as
would be the case for first order reproduction with
a very large number of speakers. So the field is
reconstructed according to the J0 and J1 functions
only, and it decays rapidly as you move away from
the reference point. In fact this would be some form
of focussing on the sweet spot.

The 'area of reconstruction' is the one were field
reconstruction is dominated by those harmonics that
are reproduced exactly rather than aliased.
Its radius is expressed in wavelengths, so for all
except LF, at least one of your ears it out of it.
At real HF this doesn't matter so much, at least
not if you have the usual random distance errors.
But there is a mid frequency range where the effect
of incorrect field reconstruction can be very marked.

Ciao,

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