Generalised Low Frequency 3D Audio Reproduction Over Loudspeakers

There exist many different techniques to reproduce 3D audio over loudspeakers, each derived from different models and motivations. However, at low frequencies these varying reproduction methods appear more similar than previously thought. This paper produces an analytical analysis of the stereo sine law, head-tracked stereo sine law, stereo tangent law/vector base amplitude panning, crosstalk cancellation and first order Ambisonics. Many of these techniques are shown mathematically to be equal or subsets of each other, resulting in a more generalised theory for low frequency audio reproduction over loudspeakers. Finally, the performance of each of the reproduction methods is considered under a low frequency analysis framework derived from a soundfield reproduction perspective.