Why Ambisonics Works

From Ambisonia

[edit] Brief Preamble

Ambisonics is a technique used to create, or to capture and recreate, a soundfield. It is firmly based on physics, mathematics and psychoacoustics. An ambisonic reproduction system will use all of the available speakers to put a sound in any location. The speaker positions are not special or preferred in any way, as is the case for other surround sound systems. The result is that the sound doesn't seem to come from the speakers, it just is there. For recording, a soundfield microphone may be used, but ambisonic signals can also be synthesised from mono sources, e.g. from a multitrack recording.

Part of the theory of ambisonics is the decomposition of a soundfield into spherical harmonics, loosely speaking a form of Fourier series on the surface of a sphere. A first order system uses four signals: W, pressure, is the only zero order component and X,Y,Z are the three first order ones. Higher order ambisonic systems use more spherical harmonics to describe the soundfield, which improves localisation and enlarges the size of the "sweet spot".

Ambisonic sound works well because it (re)creates a soundfield accurately when possible and otherwse uses an approximation that takes the psychoacoustics of sound localisation into account.

[edit] A short critique of Geoff Martin's ideas on Ambisonics

Geoff Martin's article seems to convince quite some people that there is something fundamentally wrong with Ambisonics. The article, one chapter of a much larger book, has a lot of factual errors and inaccuracies, and one can only hope that the rest of the work is somewhat better documented.

One of the most remarkable of Martin's ideas is that the first order Ambisonic components (X,Y,Z) correspond to a bidirectional microphone that has a frequency response rising by 6 dB/oct. He also isn't aware of the existence of higher order mics, even if the page was edited at the end of 2006.

In the final section titled Why Ambisonics cannot work Martin shows the impulse responses at the ears of a listener for a sound coming from the right, as reproduced by an eight-speaker regular array. He concludes that his result proves that Ambisonics cannot work because there is no significant time difference between the left and right ear signals, and because the left signal (opposite to the virtual source) has the wrong phase. His analysis is wrong on almost all accounts.

• At low frequencies (wavelenghts larger than the size of a human head), the two impulse responses will create exactly the phase difference required to tell our ears + brain that the sound is coming from the right. The antiphase signal at the left is actually helping to achieve this, and the result would be less accurate without it. Martin actually proves that Ambisonics will work, but completely fails to see, understand, or acknowledge this.

• At medium and high frequencies there is a grain of thruth in his analysis, but it's still flawed to the point of being invalid.

• • The use of shelf filters (or other methods) to modify the way a decoder works at HF has been part of Ambisonics technology almost from the start. Yet Martin uses a 'systematic' decoder for the entire frequency range, something that is strongly advised against by all authors in the field. With a correctly designed decoder the left side antiphase signal would be a lot weaker, or even completely absent.
  • The way we use inter-aural time differences in localisation is not so simple as Martin presents it. It certainly does not depend on the position of a single large peak in an impulse response, but rather on the shape of the envelope and the spectral content of the sounds that arrive at the ears.
  • In the absense of time differences, our hearing will use the amplitude difference, which is clearly present and would be larger if a correct decoder had been used.

Finally, one only has to listen to the setup used in this experiment (using a correct decoder) to note that Ambisonics does work.

FA, 6/7/2007