Antialiased soft clipping using a polynomial approximation of the integrated bandlimited ramp function

An efficient method for aliasing reduction under soft clipping using a piecewise polynomial is presented. Soft clipping is commonly used to model the saturating behavior of electronic musical systems such as guitar amplifiers and voltage-controlled filters used in subtractive synthesis. Saturations introduce high levels of harmonic distortion and, as such, are a major source of aliasing distortion which can lead to severe audible disturbances. The high level of aliasing distortion introduced by piecewise soft clippers can be mostly attributed to the discontinuities they introduce in the second and higher derivatives of the signal. The proposed method works by quasi-bandlimiting these discontinuities using a correction function defined as the integral of the bandlimited ramp (BLAMP) function. Due to the high computational costs of evaluating the analytic form of the integrated BLAMP function at every clipping point, a polynomial approximation is proposed instead. This approximation can be used to correct four samples, two on each side of every clipping point. Performance tests using sinusoidal signals show that the proposed method successfully attenuates aliasing components, particularly at low frequencies, by up to 30 dB with minimal computational costs.