In the digital simulation of non-linear audio effect circuits, the arising non-linear equation system generally poses the main challenge for a computationally cheap implementation. As the computational complexity grows super-linearly with the number of equations, it is beneficial to decompose the equation system into several smaller systems, if possible. In this paper we therefore develop an approach to determine such a decomposition automatically. We limit ourselves to cases where an exact decomposition is possible, however, and do not consider approximate decompositions.

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In this work, analog guitar amplifiers are modeled with an automated procedure using iterative optimization techniques. The digital model is divided into functional blocks, consisting of lineartime-invariant (LTI) filters and nonlinear blocks with nonlinear mapping functions and memory. The model is adapted in several steps. First the filters are measured and afterwards the parameters of the digital model are adapted for different input signals to minimize the error between itself and the analog reference system. This is done for a small number of analog reference devices. Afterwards the adapted model is evaluated with objective scores and a listening test is performed to rate the quality of the adapted models.

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Using bandlimited impulse train (BLIT) synthesis, it is possible to generate waveforms with a configurable number of harmonics with an equal amplitude. In contrast to the sinc-pulse, which is typically used for bandlimiting in BLIT and only allows to set the cutoff frequency, a Hammerich pulse can be tuned by two independent parameters for cutoff frequency and stop band roll-off. Replacing the perfect lowpass sinc-pulse in BLIT with a Hammerich pulse, it is possible to directly synthesise a multitude of signals with an adjustable lowpass spectrum.

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