In the last decades many efficient methods have been proposed to generate waveforms with reduced aliasing, proving this field quite mature. However, the introduction of Antiderivative Antialiasing (AA) methods for the reduction of aliasing in nonlinear discrete-time processing, can shed a new light on bandlimited oscillators and provide a general method for dealing with aliasing in arbitrary waveforms generation. In this work we will first bridge the gap between AA methods and bandlimited waveform generation, and then show the flexibility of the recently introduced AA-IIR method for dealing with both classical synthesizer waveforms and arbitrary wavetables. We will show how AA methods can be used for periodic and non-periodic waveform generation, and provide an innovative AA-IIR method able to compute alias-reduced version of any waveform with arbitrary antialiasing filter order, without the effort of computing ad hoc analytical expressions. Antialiasing performance is compared with other well known methods, showing the effectiveness of the approach.

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.

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 continuous-time 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.