Explicit Fixed-Point Computation of Nonlinear Delay-Free Loop Filter Networks

Abstract

An iterative method is proposed for the explicit computation of discrete-time nonlinear filter networks containing delay-free loops. The method relies on a fixed-point search of the signal values at every temporal step. The formal as well as numerical properties of fixed-point solvers delimit its applicability: On the one hand, the method allows for a reliable prediction of the frequency rates where the simulation is stable, while, on the other hand, its straightforward applicability is counterbalanced by low speed of convergence. Especially in presence of specific nonlinear characteristics, the use of a fixed-point search is limited if the real-time constraint holds. For this reason, the method becomes useful especially during the digital model prototyping stage, as exemplified while revisiting a previous discrete-time realization of the voltage-controlled filter aboard the EMS VCS3 analog synthesizer. Further tests conducted on a digital ring modulator model support the above considerations.