Ambisonie

The ambisonie is a technique of sound restitution of environment. the immersion of the user in this virtual environment is done thanks to a great number of the loudspeakers. One uses typically from ten to fifty loudspeakers. The ambisonic method exists in version 2D (the loudspeakers all are located in the horizontal plane containing the head of the user) and 3D (the loudspeakers then are often laid out on a sphere centered on the head of the user).

A system ambisonic is naturally much more powerful than a system 5.1 (home-cinema) in the field of the restitution, but it is also much more expensive in resources. It currently requires a computer dedicated in order to carry out the algorithms of spatialization in real-time.

The ambisonie is an alternative to the Holophonie, another method requiring much more loudspeaker.

Where to find a system ambisonic?

Currently, only some laboratories have a system ambisonic experimental. Generally, the laboratories are equipped only with the alternative 2D of the system. It is currently unfortunately illusory to seek a cinema having such a system. However, certain charts its make it possible to address a great number of loudspeakers and propose some simple algorithms of ambisonic restitution.

Laboratory of study in France

France Telecom studies the ambisonie for the spacialisation of the conferences in 2D (Lannion).
CSTB studies the ambisonie for the rooms of reality increased in 3D (Grenoble).

Basic principle and equations

Let us consider a system of $N \;$ loudspeakers distributed on a sphere of ray $R \;$ and directed towards the head of the user. To fix the ideas, $R \;$ often lies between 2m and 10m. One calls $O \;$ the center of the system, i.e. the point $O \;$ coincides with the head of the user.

Initially, it is reasonable to consider that the loudspeakers radiate a sound field comparable to a Onde planes. One notes

p_i (M, T) \;

pressure radiated in

M \;

by the loudspeaker

i \;

at the moment

t \;

Pressure radiated in $O \;$ is then

p (O, T) = \ sum_ {i=1} ^ {NR} p_i (O, T)

One wishes to restore the field that would create a virtual source. One notes $\ tilde p (M, T)$ this field virtual.

It is that any sound field checks the equation of Helmoltz, and can for this reason be broken up on the basis of cylindrical Harmoniques in the spherical case 2D or in the case 3D. The property to check the equation of Helmholtz is not a need for the development which follows, but it remains true.

For example one can write in 3D and for the field created by loudspeaker $i \;$

p_i (\ vec {R}, T) = G_ip_0~e^ {J (\ Omega T - K \ vec {U} _i. \ vec {R})} = \ sum \ limits_ {m \ in \ mathbb {NR}} \ sum \ limits_ {n=-m} ^m G_ip_0 Y_m^n (\ varphi_i, \ delta_i) Y_m^n (\ varphi, \ delta) j^m j_m (Kr) e^ {J \ Omega T}

where $Y_m^n (\ varphi, \ delta)$ is an administrative duty called $n \;$ ième spherical harmonic of order $m \;$ and $j_m \;$ is the spherical function of Bessel of order $m \;$ . $\ vec {R} \,$ is of course located by $(R, \ varphi, \ delta)$ in the preceding equation. $G_i$ is the profit associated with the loudspeaker $i$ .

In the same way the virtual field radiated by the virtual source is given by:

\ tilde {p} (\ vec {R}, T) = p_0~e^ {J (\ Omega T - K \ vec {U} _s. \ vec {R})} = \ sum \ limits_ {m \ in \ mathbb {NR}} \ sum \ limits_ {n=-m} ^m p_0 Y_m^n (\ varphi_s, \ delta_s) Y_m^n (\ varphi, \ delta) j^m j_m (Kr) e^ {J \ Omega T}

where $(r_s, \ varphi_s, \ delta_s)$ reference mark the position of the virtual source.

One notes now

C_ {ij} =Y_m^n (\ varphi_i, \ delta_i)

and

B_j=Y_m^n (\ varphi_s, \ delta_s)

One shows indeed that by sorting astutely the indices $(m, N) \,$ one can locate them by a single entirety $\, j$ .

Forts of this notation, the field created by the whole of the $\, N$ loudspeakers is given by

p (\ vec {R}, T) = \ sum_ {i=1} ^N \ sum_ {j=1} ^ \ infty C_ {ij} G_j

and the field to be restored is

\ tilde {p} (\ vec {R}, T) = \ sum_ {j=1} ^ \ infty B_j

One now truncates the infinite decomposition while stopping with the index $M$ . One obtains

p (\ vec {R}, T) = \ sum_ {i=1} ^N \ sum_ {j=1} ^M C_ {ij} G_j

\ tilde {p} (\ vec {R}, T) = \ sum_ {j=1} ^M B_j

The two terms are equalized, which gives in matric writing

CG=B \,

C \,

is a matrix

M \ times NR \,

. One can calculate his pseudo-opposite

D \,

. One then calculates the profits

G_j

associated with the loudspeakers by

G=DB \,

Close model of field

The real curve of the sound field radiated by high the speakers is not taken into account in this first linear model. One corrects this by filtering the signal before sending it on high the speakers.

Made error

External bonds

PhD thesis off Jerome Daniel - Memory of thesis on the ambisonie.

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