Re: [LAD] A Cathedral in your backyard

On Wed, Apr 25, 2007 at 11:33:28AM +0200, Joern Nettingsmeier wrote:

> >You say that one should antiphase the signal from the speakers in the
> >opposite direction?
>
> no. i said that "classic" ambisonics decoders do it, and it leads to
> problems in large auditoriums with listeners outside the sweet spot.

It depends on how it's done, see below.
 
> imagine you are standing off-center. all speakers start playing. two
> problems: one, if the auditorium is large, the speakers close to you
> might hit a lot earlier than those on the opposite side. if they are
> more than about 30ms apart, the haas effect kicks in and you will
> localize the sound as coming from the closer speakers.
> two, if the levels of the far and close speakers differ by more than 6-8
> db, you will localize the sound at the louder source even without the
> haas effect. not so much an issue, because such arrays carry a long way
> and the level does not drop much.

Using antiphase signals (to enhance the rV vector, i.e. and get matching
pressure and velocity magnitudes) should be done only inside the 'area of
perfect reconstruction'. In practice this means for low frequencies only,
and this is why a good Amb decoder must be dual-band.

This APR is not simply a physical area, it should be seen a as subset
of the product space (distance-to-sweet-spot, wavelength). Within that
space it is the area where distance-to-sweet-spot < R * wavelength,
with R a constant depending on the order of the system.

So in physicla space the APR is a spherical area centered on the 'sweet
spot' - the place where your Amb decoder + speakers will reconstruct the
spherical harmonics represented by the input signals - and having a radius
proportional to wavelength.

Now given a certain listening area (in terms of distance to sweet-spot),
this will be inside the APR up to a certain frequency. Within the APR,
the Haas effect and speaker amplitude ratios _do not matter_, because
you have the correct sound field, regardless of how it is constructed.

Now for low order systems this is rather academic. As R is quite small,
it's nearly impossible to have the 30 ms relative delay required for the
Haas effect, and be within the APR at the same time. But for higher order
systems this is perfectly possible. Suppose R = 2 (this requires about
order 13). At 100 Hz, the radius of the APR is 6.8 m. so you could have
a distance difference of 13.6 between two speakers of a very large
system. This corresponds to 40 ms, but there will be no Haas effect.

-- 
FA
Follie! Follie! Delirio vano è questo !
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