Antiderivative antialiasing, lagrange interpolation and spectral flatness

Abstract

Aliasing is major problem in any audio signal processing chain involving nonlinearity. The usual approach to antialiasing involves operation at an oversampled rate—usually 4 to 8 times an audio sample rate. Recently, a new approach to antialiasing in the case of memoryless nonlinearities has been proposed, which relies on operations over the antiderivative of the nonlinear function, and which allows for antialiasing at audio or near-audio rates, and without regard to the particular form of the nonlinearity (i.e., polynomial, or hard clipping). Such techniques may be deduced through an application of Lagrange interpolation over unequally-spaced values, and, furthermore, may be constrained to behave as spectrally transparent “throughs” for nonlinearities which reduce to linear at low signal amplitudes. Numerical results are presented.