Wave Digital Extended Fixed-Point Solvers for Circuits With Multiple One-Port Nonlinearities

Wave Digital Filter (WDF) theory has been widely used to design nonlinear digital filters that behave like reference analog circuits, especially in the field of Virtual Analog modeling, i.e., the digital emulation of audio circuits. WDF principles allow us to implement circuits with one nonlinearity in an explicit fashion, by properly setting the free parameters that are introduced in the Wave Digital (WD) domain. Although this property does not extend to the WDF realization of circuits with multiple nonlinearities, which instead requires the use of iterative solvers, a proper setting of the free parameters is beneficial also in these cases, in terms of both robustness and efficiency of the implementation. In particular, recent research shows that a common optimal policy for the setting of free parameters can be adopted when either a WD fixed-point method or a WD Newton-Raphson (NR) method is used to solve the same nonlinear circuit. In this work, we present a class of WD extended fixed-point solvers with order from zero to infinity that generalizes the aforementioned iterative methods; the zero-order case corresponds to the existent WD fixed-point method, while the infinite-order case to WD NR. The proposed solvers do not require to compute inverse Jacobian matrices and are characterized by superlinear speed of convergence. Moreover, we show that the very same policy of free parameter setting can be applied independently of the order, causing, in any case, an increase of robustness and convergence speed.