It is not difficult to find equations for how to encode a mono source onto 1st order (B-format) ambisonics. Unfortunately it’s much more difficult to find equations for decoding. Furse has made available decoding parameters for some standard symetrical loudspeaker setups but from there to a more general solution it is hard to figure out what to do. Also his equations is nothing but a gain matrix there’s no taking into account phases or shelf filters. (BTW there are some details on hilbert and shelf filters in this mail) Malham discuss the issue in an article in Organized Sound 3(2) 1998.000 According to that article one of the most thorough discussions of decoding was done in an article by Gerzone in 1992 (Gerzon M. A. 1992.000 Psychoacoustic decoders for multispeaker stereo and surround sound. Preprint No. 3406 92nd Convention of the Audio Engineering Society).
There’s also a lengthy discussion on decoding and copyright issues in the Sursound mailing list archive from July and August 2002 but unfortunately with little or no details on how to do the decoding. It turns out that technology for decoding to an array of irreguarly positioned loudspeakers generally known as the Vienna technology is patented by Trifield Productions Limited. The actual patent can be found here: US patent United States Patent 5757927: Surround sound apparatus issued in 1998.000 The patent holder Geoffrey Barton gives the following abstract of the patent:
The Vienna decoder could be summarised as an Ambisonic decoder where the values
of thetaV and thetaE are arranged to be substantially the same but that (a) high
frequency rv varies with direction and (b) the pressure directional gain pattern
varies with frequency thus giving the desirable aspects of an Ambisonic decoder
but (in the case of a 5.100 decoder) preference to the front stage.
Items (a) and (b) distinguish it from conventional Ambisonic decoder solutions.
Searching through the list archives of the sursound mailing list I also found some equations describing how to do forward dominance a kind of “zoom control” that moves the listener forwards or backwards in the sound field. One of the possibilities that I and Justin discussed while he was in Bergen was the ability of moving around in a field of surround sources. This is the closest I’ve come to see any equations expressing how to do it.
