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

Loudspeaker virtualization–Part I: Digital modeling and implementation of the nonlinear transducer equivalent circuit

“…It follows that the proposed WDF can be integrated in digital signal processing algorithms for linearization, equalization, or, more generally, virtualization of loudspeakers. This will be demonstrated in the second part of this two-part work [43].…”

“…The considered nonlinear model is then realized using a novel fully explicit WDF which does not require any iterative solver to be implemented. The WDF discussed in this manuscript is an essential building block of the loudspeaker virtualization algorithm extensively described in the second part [43] of this two-part work. The present manuscript is therefore self-contained, even though important applications of the presented WDF model of loudspeakers are discussed in the companion article [43].…”

On the Virtualization of Audio Transducers

“…Such algorithms are based on general signal processing chains which can be exploited to perform all the traditional tasks envisaged by the algorithms mentioned in the previous paragraph, e.g., linearization and equalization. Recently, loudspeaker virtualization has been tackled by using a digital signal processing approach based on physical modeling [16,17], which exploits the inverse model of the loudspeaker equivalent circuit. The design of the inverse system relies on Leuciuc's theorem [18], reworded in [16,19], and it is derived by duly adding to the direct circuital system a theoretical two-port element, known in circuit theory as nullor.…”

“…The digital inverse system can then be used to compensate for the behavior of the physical loudspeaker and, hence, impose the behavior of a digital target system. This is achieved by implementing the so called Direct-Inverse-Direct Chain [17] composed of a target direct system, which is a digital filter characterized by the desired transduction behavior to be imposed; the inverse loudspeaker system, which is a digital filter whose response is the inverse of that of the physical transducer; and the (direct) phyisical loudspeaker. While in the approach of [16,17] inversion is digitally attained, other methods to design inverse circuital systems, which rely on analog filters or integrated circuits, such as operational transconductance amplifiers, current conveyors, current differencing buffered amplifiers, etc.…”

“…In [25], vector waves are used to derive a vectorial scattering relation that allows to implement a nullor as a two-port input-output element in the WD domain. Moreover, in [16,17], it has already been shown that WDFs are suitable to efficiently emulate direct and inverse models of nonlinear loudspeakers in the discrete-time domain with no need of iterative solvers.…”