Antialiasing Piecewise Polynomial Waveshapers
Memoryless waveshapers are commonly used in audio signal processing. In discrete time, they suffer from well-known aliasing artifacts. We present a method for applying antiderivative antialising (ADAA), which mitigates aliasing, to any waveshaping function that can be represented as a piecewise polynomial. Specifically, we treat the special case of a piecewise linear waveshaper. Furthermore, we introduce a method for for replacing the sharp corners and jump discontinuities in any piecewise linear waveshaper with smoothed polynomial approximations, whose derivatives match the adjacent line segments up to a specified order. This piecewise polynomial can again be antialiased as a special case of the general piecewise polynomial. Especially when combined with light oversampling, these techniques are effective at reducing aliasing and the proposed method for rounding corners in piecewise linear waveshapers can also create more “realistic” analog-style waveshapers than standard piecewise linear functions.