Ambisonics

Introduction & Theory

Ambisonics was a system pioneered mainly by Michael Gerzon and is based on the spherical harmonic decomposition of a sound field (Gerzon, 1974). In order to understand this last statement the fundamentals of Ambisonics are reviewed.

A definition for what makes a decoder Ambisonic can be found in Gerzon & Barton (1992) and their equivalent U.S. patent regarding Ambisonic decoders for irregular arrays (Gerzon & Barton, 1998), and states (slightly adapted to remove equations):

A decoder or reproduction system is defined to be Ambisonic if, for a centrally seated listening position, it is designed such that:
1. The decoded velocity and energy vector angles agree and are substantially unchanged with frequency.
2. At low frequencies (below around 400 Hz) the low frequency velocity vector magnitude is equal to 1 for all reproduced azimuths
3. At mid/high frequencies (between around 700 Hz and 4 kHz) the energy vector magnitude is substantially maximised across as large a part of the 360° sound stage as possible.

To understand these statements, the underlying concepts of Ambisonics will be explained, leading into a description of the velocity and energy vectors and their relevance to multi-speaker surround sound systems.

BlumleinF8small.JPGAmbisonics is a logical extension of Blumlein’s binaural reproduction system (at least, after it’s conception). Probably one of the most forward looking features of the Blumlein technique is that when using the two figure of eight capsules positioned perpendicular to each other (as shown on the left), any other figure of eight response could be created (it was this fact that was utilised in Blumlein’s spatial equalisation technique - see Blumlein Stereo). The equation used to calculate a figure of eight pointing in direction ø is shown below:

Equation_Figure8.GIFwhere: ø is the desired response angle.
L is the left facing figure of eight microphone.
R is the right facing figure of eight microphone.
Figure8 is the reconstructed figure of eight microphone.

This approach is very similar to Gerzon’s in that the encoding (recording) side is independent from the decoding (reproduction) process. That is, Blumlein stereo could be replayed over 1, 2 or more speakers. Where Gerzon’s Ambisonics improves upon this idea is as follows:
  • Ambisonics can be used to recreate a full three dimensional sound field (i.e. height information can also be extracted from the Ambisonics system).
  • The decoded polar pattern can be changed, that is, you are not fixed to using a figure of eight response.

BFormat.JPGAs an example, 1st order Ambisonics can record a sound field using four signals (collectively known as B-Format). The W signal is an omni-directional pressure signal that represents the zeroth order component of the sound field and X, Y and Z are figure of eight microphones used to record the particle velocity in any one of the three dimensions. Graphical representations of these four B-Format microphone signal responses are shown to the right.

Ambisonics is a hierarchical format so that although four channels are needed for full three-dimensional reproduction, only three channels are needed if the final replay system is a horizontal only system. The mathematical equations representing the four microphone responses used in B Format are shown in the equation below. These equations can also be used to encode a sound source and represent the gains applied to the sound for each channel of the B-format signal.
Equation_BFormat.GIF

where:
alpha = elevation angle of the source.
theta = azimuth angle of the source.
In order to replay a B-Format signal, virtual microphone responses are calculated and fed to each speaker. That is, using the B-format signals, any 1st order microphone response can be obtained pointing in any direction. This is very much like the theory behind Blumlein Stereo, except that you can choose the virtual microphone response from any first order pattern (and not just a figure of eight), from omni to figure of eight. This is possible using the simple equation shown below (Farina et al., 2001)

References

Farina, A. et al. (2001) Ambiophonic Principles for the Recording and Reproduction of Surround Sound for Music. Proceedings of the 19th AES International Conference of Surround Sound, Schloss Elmau, Germany, p. 26-46.
Gerzon, M. A. (1974a) Sound Reproduction Systems. Patent No. 1494751.
Gerzon, M. A. & Barton, G. J. (1992) Ambisonic Decoders for HDTV. Proceedings of the 92nd International AES Convention, Vienna. 24 – 27 March. Preprint 3345.
Gerzon, M.A, Barton, G.J. (1998) Surround Sound Apparatus. U.S. Patent No. 5,757,927