The generation of panning laws for irregular speaker arrays using heuristic methods

Currently, the ITU standard surround sound speaker arrangement is based on an irregular 5 speaker array. However, this may change to an irregular 7 speaker array (as is now the standard on computer hardware) or more in the future. The Ambisonic system, pioneered by Micheal Gerzon, among others, in the late 1960’s, is very well suited to situations where the end system speaker configuration is not fixed in terms of number or position while also offering a simple way (via energy and velocity vector analysis) of quantifying the performance of such systems. However, while the derivation of the decoders is well documented for regular speaker arrangements [1], optimising the decoders for irregular layouts is not a simple task, where optimisation requires the solution of a set of non linear simultaneous equations, complicated further by the fact that multiple solutions are possible [2]. Craven [3] extended the system to use higher order circular harmonics and presented a 4th order Ambisonic decoder (9 input channels), although the derivation method used was not presented. In this paper a semi-automated decoder optimisation system using heuristic methods will be presented that will be shown to be robust enough to generate higher order Ambisonic decoders based on the energy and velocity vector parameters. This method is then analytically compared to Craven’s decoder using both energy/velocity vector and head related transfer function based methods.