# Understanding Ambisonics Signals

## Spherical Harmonics

Ambisonics is based on a decomposition of a sound field into spherical harmonics. These spherical harmonics encode the sound field according to different axes, respectively angles of incidence. The number of Ambisonics channels $N$ is equal to the number of spherical harmonics. It can be calculated for a given order $M$ with the following formula:

\begin{equation*} N = (M+1)^2 \end{equation*}

Figure 1 shows the first 16 spherical harmonics. The first row ($N=1$) is the omnidirectional sound pressure for the order $M=0$. Rows 1-2 together represent the $N=4$ spherical harmonics of the first order Ambisonics signal, rows 1-3 correspond to $M=2$, respectively $N=9$ and rows 1-4 to the third order Ambisonics signal with $N=16$ spherical harmonics. First order ambisonics is sufficient to encode a threedimensional sound field. The higher the Ambisonics order, the more precise the directional encoding.

Fig. 1: Spherical harmonics up to order 3 1.

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https://commons.wikimedia.org/wiki/Category:Spherical_harmonics#/media/File:Spherical_Harmonics_deg3.png

## Ambisonic Formats

An Ambisonics B Format file or signal carries all $N$ spherical harmonics. Figure 2 shows a first order B Format signal.

Fig. 2: Four channels of a first order Ambisonics signal.

There are different conventions for the sequence of the individual signals, as well as for the normalization.

### References

#### 2015

• Matthias Frank, Franz Zotter, and Alois Sontacchi. Producing 3d audio in ambisonics. In Audio Engineering Society Conference: 57th International Conference: The Future of Audio Entertainment Technology–Cinema, Television and the Internet. Audio Engineering Society, 2015.
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