Analytical driving functions for higher order Ambisonics

In this paper, we present the derivation and investigation of analytical expressions for the loudspeaker driving signals for higher order Ambisonics. The approach relies on the assumption of a continuous distribution of secondary sources on which sampling is performed to yield the actual loudspeaker signals for real-world implementations. For source-free volumes enclosed by the secondary source distribution, this formulation of Ambisonics leads to what is known as simple source approach. Since the simple source approach is theoretically well documented, we will depart from it and concentrate on the special case of a circular distribution of secondary point sources and derive analytical expressions for the driving signals. We furthermore derive a closed-form expression for the actual reproduced wave field for the circular secondary source distribution.