2.5D higher order ambisonics for a sound field described by angular spectrum coefficients

This paper derives an analytical solution to convert sound field representation from the angular spectrum to the circular harmonics expansion. A sound field is decomposed to plane waves by the spatial Fourier transform and represented by the angular spectrum. A plane wave is also described by the circular harmonics expansion. In the proposed formulation, these two representations are integrated and a sound field can be represented by the circular harmonics expansion with the angular spectrum coefficients. For actual implementations, the driving function of a circular sound source for 2.5D higher order Ambisonics is analytically derived from a sound field described by the angular spectrum. The results of the computer simulations show that the proposed method with a circular loudspeaker array can reproduce a sound field recorded by a linear microphone array with appropriate accuracy around the center of the circular array.