Nonlinear digital circuits and waveshaping are active areas of study, specifically for what concerns numerical and aliasing issues. In the past, an effective method was proposed to discretize nonlinear static functions with reduced aliasing based on the antiderivative of the nonlinear function. Such a method is based on the continuoustime convolution with an FIR antialiasing filter kernel, such as a rectangular kernel. These kernels, however, are far from optimal for the reduction of aliasing. In this paper we introduce the use of arbitrary IIR rational transfer functions that allow a closer approximation of the ideal antialiasing filter, required in the fictitious continuous-time domain before sampling the nonlinear function output. These allow a higher degree of aliasing reduction and can be flexibly adjusted to balance performance and computational cost.

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Fractional order filters have been studied since a long time, along with their applications to many areas of physics and engineering. In particular, several solutions have been proposed in order to approximate their frequency response with that of an ordinary filter. In this paper, we tackle this problem with a new approach: we solve analytically a simplified version of the problem and we find the optimal placement of poles and zeros, giving a mathematical proof and an error estimate. This solution shows improved performance compared to the current state of the art and is suitable for real-time parametric control.

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Employing nonlinear functions in audio DSP algorithms requires attention as they generally introduce aliasing. Among others, antiderivative antialiasing proved to be an effective method for static nonlinearities and gave rise to a number of variants, including our AA-IIR method. In this paper we introduce an improvement to AA-IIR that makes it suitable for use in stateful systems. Indeed, employing standard antiderivative antialiasing techniques in such systems alters their frequency response and may cause stability issues. Our method consists in cascading a digital filter after the AA-IIR block in order to fully compensate for unwanted delay and frequency-dependent effects. We study the conditions for such a digital filter to be stable itself and evaluate the method by applying it to the diode clipper circuit.

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Hard sync is a feature appearing in many analog synthesizers: it consists in retriggering a slave oscillator, regardless of its phase, every time a master oscillator completes its cycle. If this process is naïvely implemented digitally, it is subject to aliasing. While for sawtooth, square, and triangle waves several effective antialiasing methods have been developed, the literature is sparser concerning sine hard sync, arguably because discontinuities of infinite order are introduced which are more difficult to handle. In this paper, we introduce a new antialiasing algorithm for sine hard sync which is obtained by filtering the hard-synced sine with a FIR lowpass kernel, as opposed to existing methods based on the windowed sinc function. We show that our method yields lower computational cost and better aliasing reduction.

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