Fabian Esqueda

Aliasing Reduction in Clipped Signals

An aliasing reduction method for hard-clipped sampled signals is proposed. Clipping in the digital domain causes a large amount of harmonic distortion, which is not bandlimited, so spectral components generated above the Nyquist limit are reflected to the baseband and mixed with the signal. A model for an ideal bandlimited ramp function is derived, which leads to a postprocessing method to reduce aliasing. A number of samples in the neighborhood of a clipping point in the waveform are modified to simulate the Gibbs phenomenon. This novel method requires estimation of the fractional delay of the clipping point between samples and the first derivative of the original signal at that point. Two polynomial approximations of the bandlimited ramp function are suggested for practical implementation. Validation tests using sinusoidal, triangular, and harmonic signals show that the proposed method achieves high accuracy in aliasing reduction. The proposed 2-point and 4-point polynomial correction methods can improve the signal-to-noise ratio by 12 and 20 dB in average, respectively, and are more computationally efficient and cause less latency than oversampling, which is the standard approach to aliasing reduction. An additional advantage of the polynomial correction methods over oversampling is that they do not introduce overshoot beyond the clipping level in the waveform. The proposed techniques are useful in audio and other fields of signal processing where digital signal values must be clipped but aliasing cannot be tolerated.

Aliasing reduction in soft-clipping algorithms

Soft-clipping algorithms used to implement musical distortion effects are major sources of aliasing due to their nonlinear behavior. It is a research challenge to design computationally efficient methods for alias-free distortion without over-sampling. In the proposed approach, soft clipping is decomposed into a hard clipper and a low-order polynomial part. A technique for aliasing reduction of the hard-clipped signal is presented based on a polynomial approximation of the ban-dlimited ramp function. This correction function operates by quasi-bandlimiting the discontinuities introduced in the first derivative of the signal. The proposed method effectively reduces perceivable aliasing in soft-clipped audio signals having low frequency content. This work presents the first step towards alias-free implementations of nonlinear virtual analog effects.

Antiderivative antialiasing, lagrange interpolation and spectral flatness

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.

Antialiased soft clipping using an integrated bandlimited ramp

A new method for aliasing reduction in soft-clipping nonlinearities is proposed. Digital implementations of saturating systems introduce harmonic distortion which, if untreated, gets reflected at the Nyquist limit and is mixed with the signal. This is called aliasing and is heard as a disturbance. A new correction function, derived by integrating the bandlimited ramp function, is presented. This function reduces the level of aliasing distortion seen at the output of soft clippers by quasi-bandlimiting the discontinuities introduced in the second derivative of the signal. The proposed method increases the quality of the signal by attenuating those aliased components that lie on the lower end of the spectrum, which are known to be perceptually important. The four-point version of the algorithm reduces aliasing at low frequencies by up to about 50 dB. This work extends our understanding of aliasing in nonlinear systems and provides a new tool for its suppression in virtual analog models.