Reproduction of focused sources by the spectral division method

Sound reproduction methods based on the physical resynthesis of a desired field using loudspeaker arrays are well-established nowadays. Their physical basis allows to resynthesize almost any desired wave field, even the field of sound sources positioned in between the loudspeakers and the listener. Such sources are known as focused sources. This paper will present a novel approach to the reproduction of focused sources with linear loudspeaker arrays. Its formulation is based on a representation of the respective fields in the spatio-temporal frequency domain. The derivation of the loudspeaker driving function is discussed, as well as a number of practical limits, the role of evanescent contributions and the connections to other established techniques.