# 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:

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.

## Ambisonic Formats

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

[details] [BibTeX▼]

#### 2009

- Frank Melchior, Andreas Gräfe, and Andreas Partzsch.
**Spatial audio authoring for ambisonics reproduction.**In*Proc. of the Ambisonics Symposium*. 2009.

[details] [BibTeX▼]