We propose a new analog filter discretization method that is useful for discretizing systems with features near or above the Nyquist limit. A conformal mapping approach is taken, and we introduce the peaking conformal map and shelving conformal map. The proposed method provides a close match to the original analog frequency response below half the sampling rate and is parameterizable, order preserving, and agnostic to the original filter’s order or type. The proposed method should have applications to discretizing filters that have time-varying parameters or need to be implemented across many different sampling rates.

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Herein, we demonstrate the use of neural nets towards simulating multiport nonlinearities inside a wave digital filter. We introduce a resolved wave definition which allows us to extract features from a Kirchhoff domain dataset and train our neural networks directly in the wave domain. A hyperparameter search is performed to minimize error and runtime complexity. To illustrate the method, we model a tube amplifier circuit inspired by the preamplifier stage of the Fender Pro-Junior guitar amplifier. We analyze the performance of our neural nets models by comparing their distortion characteristics and transconductances. Our results suggest that activation function selection has a significant effect on the distortion characteristic created by the neural net.

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