Loudspeaker virtualization–Part II: The inverse transducer model and the Direct-Inverse-Direct Chain

This manuscript, the second of a two-part series, shows how a discrete-time circuital model of loudspeakers, which is extensively analyzed in the first part, can be exploited to develop a method for loudspeaker virtualization. This method can be used to alter the behavior of a physical loudspeaker in such a way to match that of a target loudspeaker. Examples of applications include loudspeaker equalization or linearization. The method is characterized by a structure called Direct-Inverse-Direct Chain, which is composed of three blocks: a digital model of the target loudspeaker; a digital model of the inverse loudspeaker; and the physical loudspeaker. The inverse loudspeaker model is derived from the equivalent circuit of the direct system using a two-port element known in circuit theory as "nullor". We show how this inverse model can be efficiently implemented in the discrete-time domain with no iterative solvers by exploiting Wave Digital Filter principles. The proposed virtualization algorithm is extensively tested both through simulations and applications to real loudspeakers. In particular, we show how the algorithm can reduce the distortion of the transducer output pressure signal, and how it can make a loudspeaker sound like a target loudspeaker with a desired nonlinear behavior.