Hi again,
Date: Thu, 21 Jul 2011 12:45:45 -0000
From: Richard Lee <rica...@justnet.com.au>
It is true that 1st order ambisonics doesn't consider distance,
with all
sources being reproduced at the distance of the speakers,
.....
synthesis, the ambisonic encoding equations do not include distance,
Both of these are untrue.
For the second, see the Appendix of BLaH3 "Is my decoder
Ambisonic?" Heller
et al, AES San Francisco, 2008
Looking again at the equations, it is not so clear. As normally
expressed in cartesian coordinates (x,y,z, all limited to values
between -1 and +1) they do within the unit sphere (the distance of
the speakers), but in polar coordinates there is unity magnitude of
the vector, and everything is on the unit sphere.
These equations are only really useful when we wish to pan a mono
source ambisonically, what might be called spatial synthesis or
coding. Within the unit sphere they lead to 2nd and above components
going to zero at zero distance, and Gerzon/Malham?? suggested
increasing W inside the sphere to maintain the same apparent loudness.
There is certainly no consideration of values outside the unit
sphere. To take just the 1st order, the X signal in cartesian
coordinates = S*x, S being the amplitude of the source and x its
front/back distance. This would lead to increasing amplitude of the X
signal with distance, obviously the opposite of what is observed.
So any attempt to simulate distance has to rely on other descriptions
of what happens physically. In anechoic conditions a good start is
the inverse square law: amplitude varies with 1/d. We can get round
the problem of this going to infinity at zero distance by simply
adding 1, so the listener is at distance 1, and the speakers at
distance 2. This somehow fits with a curious ambisonic paradox: the
microphone and the listener are at distance zero, and the speakers at
distance 1.
This leads to the energy being 6dB lower at the speaker distance, and
unity gain at zero. Without some sort of reverb model this sounds
much too extreme, and many prefer a 1/sqrt(d) law, rather curiously
the law that Chowning suggests for the amplitude of indirect
reflected sound.
There are two convenient proofs of the fallacy of the first.
I admit to not being careful enough in my phrasing of my assertion.
The B-Format (or higher order) signals, rather than the original
sound sources, are reproduced at the distance of the speakers. I
thought that I had also written (though obviously omitted to) that
recordings, and microphone signals in general, contain distance
information: they reproduce what would be heard acoustically to a
greater or lesser degree.
So, I agree with what you say, though I was talking about ambisonic
synthesis and should have made that clearer.
While making a normal recording, creep silently up to your TetraMic or
Soundfield and whisper into it.
When you play this back to an unsuspecting victim seated in the
centre of a
simple Classic Ambisonic rig, he will flinch. He certainly doesn't
hear
you at the radius of the speakers.
The other 'proof' is the B-format motorcycle that Soundfield have
played at
nauseum at various shows. Ambisonic myth has it that this was
recorded by
the young Dr. Peter Lennox on Grand Vizier Malham's modified Calrec
Soundfield Mk 3A while the Vizier was away on a diplomatic visit to
the
Great Turtle that Supports the Universe. This mike was one of the
first to
have IMHO, the proper EQ which allow a Soundfield to implement the
correct
Ambisonic Encoding Eqns in the Appendix of BLaH3.
Ciao,
Dave Hunt
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