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.

Antiderivative Antialiasing for Stateful Systems

“…It should be noted that the extensions to higher-order antiderivatives as proposed in [14] or [15] should be straightforward, following the same principle. A more interesting future direction would be to lift the restriction on the nonlinear function to have only scalar or very-low-dimensional input.…”

“…A more interesting future direction would be to lift the restriction on the nonlinear function to have only scalar or very-low-dimensional input. If the method of [10] (or even the higher-order extensions of [14] or [15]) could be generalized to nonlinear functions with multiple inputs without requiring excessively large lookup tables, the method proposed in the present paper would immediately generalize to all stateful nonlinear systems.…”

Antiderivative Antialiasing Techniques in Nonlinear Wave Digital Structures

“…In pth-order ADAA, the approximation f of f introduces a delay of p/2 samples [31], causing the waves incident to the junction in vector b[k] to be misaligned in time. Therefore we need to apply synchronization delays, similarly to what was done in (7).…”

“…A possible metric to measure the suppression of the aliased components with respect to desired harmonic distortion components of the clipping stage is the Signal-to-Noise Ratio (SNR), here defined as a power ratio between the desired harmonic components and the aliased components. The SNR analysis has been performed as described in [25,31] for a set of sinusoidal inputs at different fundamental frequencies, ranging from 1 kHz to 10 kHz. For each test signal an ideal alias-free version was obtained by calculating the discrete-time Fourier transform at integer multiples of the fundamental frequency up to the Nyquist frequency and using additive synthesis.…”

“…Nonetheless ADAA presents two major drawbacks: a low-pass filtering effect and the introduction of a fractional delay of p/2 samples [31]. The first limitation can be easily overcome through mild oversampling or by designing a simple linear filter.…”