Because many elements of audio systems display nonlinearities, it is important to understand and model their behavior. The usual way to model such nonlinearities uses Volterra series and its subclass, polynomial Hammerstein model(s), which is a cascade of M parallel branches composed of a static monomial nonlinearity followed by linear filters. Unfortunately, the cascade of Hammerstein models manifests a large sensitivity to implementation inaccuracies, especially when the order M increases. This paper highlights different kinds of errors and shows how they can affect emulation accuracy. The authors propose a way to get around each problem thereby leading to an accurate emulation of three nonlinear systems: the Tubes-Screamer like overdrive effect, the TSA15h tube amplifier, and the Engl Retro Tube 50 E762 amplifier. A solution is also provided for cases of input amplitude dependence, which appears valid for some devices. The described method appears to be suitable for real-time emulation of audio nonlinear systems.
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