The observation space and realizations of finite Volterra series
SIAM Journal on Control and Optimization
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Nonlinear Control Systems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Oscillator and Filter Algorithms for Virtual Analog Synthesis
Computer Music Journal
The Volterra and Wiener Theories of Nonlinear Systems
The Volterra and Wiener Theories of Nonlinear Systems
A review of digital techniques for modeling vacuum-tube guitar amplifiers
Computer Music Journal
IEEE Transactions on Signal Processing - Part I
Discrete-time modelling of the moog sawtooth oscillator waveform
EURASIP Journal on Advances in Signal Processing - Special issue on musical applications of real-time signal processing
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Volterra series are known to be efficient to represent weakly nonlinear systems and the first distortions. Their truncated versions allow one to derive realizations (in the sense of system theory) leading to networks composed of linear filters, sums, and instantaneous products of signals, without instantaneous feedback loops. Nevertheless, if saturation phenomena arise, truncating the series at low order is not sufficient and the convergence can also be lost. In this paper, the case of the Moog ladder filter is investigated. Low-cost simulations based on realizations of Volterra series are given. Their limitations with respect to the amplitude of input signals are exhibited. Methods to increase the validity range and to improve the efficiency of Volterra series expansions are detailed on a single stage of the filter. In particular, changes of states based on the difference between the original state and predictors (parameterized by a tunable delay T) yield satisfying results. The digital simulation of this system preserves the properties mentioned above. It includes two delay lines (where the delay T can be chosen to be one sample) and nonlinear static functions given by the method.