Ambisonic Decoding With Constant Angular Spread

Ambisonic decoding refers to the process of reconstructing a sound field represented by spherical harmonic modes up to a given order. The issue with the spherical harmonic representation is that perfect reconstruction of the sound field is typically possible only within an area whose size is inversely proportional to the frequency. Therefore, in order to decode ambisonic signals for high-frequency sounds or a wide listening area, one has to rely on other criteria than the sound field reconstruction error. Classic criteria for the derivation of ambisonic decoding matrices are the total energy of the loudspeaker signals and the direction and norm of the so-called energy vector, which corresponds to the energy-weighted sum of the unit vectors pointing to the directions of the loudspeakers. The underlying idea behind using such criteria is that they are somewhat related to the perceptual attributes of the reproduced sound field. In particular, the norm of the energy vector can be interpreted in terms of the angular spread of energy across loudspeakers, which was recently shown to be correlated to the perceived width of virtual sources. In previous works, ambisonic decoding methods have been presented which yield a constant loudspeaker energy and minimal energy-vector direction mismatch across virtual source directions. However, in the case of irregular speaker layouts, these methods result in a varying angular spread across directions. In this paper we present a method for calculating ambisonic decoding matrices providing a nearly constant angular spread across source directions while maintaining a constant energy and very low energy-vector direction mismatch.