I think one can figure out something here without too much mathematical
analysis about what is missing in first order.
It is similar to what is missing in Blumlein stereo.
Namely if a hard transient occurs say 30 degrees left of center,
the associated wavefront arrives at the left ear before
it arrives at the right ear.
The phase part of this in the phase sensitive region (below around 1k) is
reconstructed correctly via head shadowing in Blumlein playback.
But the high frequency transient part is not.
This high frequency transient part--literal transient arrival time
as opposed to phase information in the phase sensitive region--
is audible directly. Ambisonic people do not much like to discuss this
fact in my experience, but a fact it is.
The problem with spaced microphones , not widely spaced but
just spaced apart by the interaural acoustic distance(a la ORTF),
is that they generate the phase part twice over--they get
transient time right but get phase below 1k wrong(and amplitude
a little wrong as well). People that are really with it on
the sounds of musical instruments--conductors for example--
tend to find Blumlein less colored for this reason.
But the transient time of arrival part is wrong.
This can be dealt with in Ambisonics only by using higher
order--and I think quite a lot higher order.
It is just not true that first order gets the sound right in a
neighborhood of a point. It is right only at one point. And this is
imperfect by nature. Maybe it does not bother people so much--
I like it myself. But it is not really right--unless you are
a Cyclops on the aural front.
Robert
On Thu, 25 Apr 2013, Fons Adriaensen wrote:
On Thu, Apr 25, 2013 at 02:50:24PM -0600, Bearcat M. ??ndor wrote:
As i'm still learning about Ambisonics (mostly trying to wrap my fuzzy head
around the math), there's something i don't understand.
If the 4 channels of a b-format mic give you all you need for the
mathematical computations for 3-D space, why do we have Ambisonic mics with
more than 4 channels and orders with 8, 16 and more channels? What does
having a 4 channel (w, x, y and z) mic restrict you?
There is no simple answer to your question.
As Sampo as already pointed out, first order AMB signals provide
all the info there is about the sound field in a single point.
The physics and maths being what they are, they also define the
sound field in an area around that point. The size of that area
depends on the frequency. For first order the 'extrapolation'
works well up to a distance of around 1/4 to 1/3 of a wavelength.
So the area it covers will be quite large at low frequencies (LF),
but gets very small for medium (MF) and high (HF) frequencies.
Above a few hundred Hz it is so small that it is impossible even
for a single listener to have both ears inside the area in which
the sound field is accurately reconstructed.
So for MF and HF Ambisonic decoders use an ad-hoc approximation
which is based on psycho-acoustics and which works well in practice.
That is the reason why you need a frequency-dependent decoder,
either dual-band or using shelf filters. So far for first order.
Higher order Ambisonics provides two things. First, the area in
which the sound field is reconstructed 'exactly' becomes larger,
more or less proportional to order. But in practice little is gained
from this and we still need the 'approximation' for the mid and high
frequency range. But HOA also allows this approximation to be much
more accurate, to the point that for third order or above, in practice
it can be 'almost perfect'. This allows HOA to work in a much larger
listening area than first order, i.e. to serve a large audience, and
also to be usable in situations were for practical reasons (related
to speaker placement) first order would not work well.
To really fully understand the why and how you'll need the maths.
What I wrote above is an attempt to explain things in intuitive
terms, which means to simplify things, but hopefully not to the
point where the essence is lost.
Ciao,
--
FA
A world of exhaustive, reliable metadata would be an utopia.
It's also a pipe-dream, founded on self-delusion, nerd hubris
and hysterically inflated market opportunities. (Cory Doctorow)
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