Conversion of multichannel sound signals based on spherical harmonics with L1-norm constraint

This paper proposes a novel method for converting multichannel signals of an original system into that of an alternative system. Based on spherical harmonics expansion, we present a conversion formulation to derive matching equation which explains a direct relationship between weighting matrix and positions of loudspeakers located on both systems. The solution of matching equation can be found from matrix inverse where under-determined problem might exist. To solve this problem, l₁-norm minimization is proposed for finding a minimum number constraint of the active loudspeakers. Simulations confirm that the proposed method is able to reconstruct original sound field within a finite region of listening and has better wideband performance than traditional method.