Paper Archive

Neural networks have become ubiquitous with guitar distortion effects modelling in recent years. Despite their ability to yield perceptually convincing models, they are susceptible to frequency aliasing when driven by high frequency and high gain inputs. Nonlinear activation functions create both the desired harmonic distortion and unwanted aliasing distortion as the bandwidth of the signal is expanded beyond the Nyquist frequency. Here, we present a method for reducing aliasing in neural models via a teacher-student fine tuning approach, where the teacher is a pretrained model with its weights frozen, and the student is a copy of this with learnable parameters. The student is fine-tuned against an aliasing-free dataset generated by passing sinusoids through the original model and removing non-harmonic components from the output spectra. Our results show that this method significantly suppresses aliasing for both long-short-term-memory networks (LSTM) and temporal convolutional networks (TCN). In the majority of our case studies, the reduction in aliasing was greater than that achieved by two times oversampling. One side-effect of the proposed method is that harmonic distortion components are also affected. This adverse effect was found to be modeldependent, with the LSTM models giving the best balance between anti-aliasing and preserving the perceived similarity to an analog reference device.

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Efficient stable integration methods for nonlinear systems are of great importance for physical modeling sound synthesis. Specifically, a number of musical systems of interest, including vibrating strings, bars or plates may be written as port-Hamiltonian systems with quadratic kinetic energy and non-quadratic potential energy. Efficient schemes have been developed for such systems through the introduction of a scalar auxiliary variable. As a result, the stable real-time simulations of nonlinear musical systems of up to a few thousands of degrees of freedom is possible, even for nearly lossless systems. However, convergence rates can be slow and seem to be system-dependent. Specifically, at audio rates, they may suffer from numerical drift of the auxiliary variable, resulting in dramatic unwanted effects on audio output, such as pitch drifts after several impacts on the same resonator. In this paper, a novel method for mitigating this unwanted drift while preserving power balance is presented, based on a control approach. A set of modified equations is proposed to control the drift artefact by rerouting energy through the scalar auxiliary variable and potential energy state. Numerical experiments are run in order to check convergence on simulations in the case of a cubic nonlinear string. A real-time implementation is provided as a Max/MSP external. 60-note polyphony is achieved on a laptop, and some simple high level control parameters are provided, making the proposed implementation suitable for use in artistic contexts. All code is available in a public repository, along with compiled Max/MSP externals1.

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Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string, where geometric nonlinear effects lead to perceptually important effects including pitch glides and a dependence of brightness on striking amplitude. A modal decomposition leads to a coupled nonlinear system of ordinary differential equations. Recent work in applied machine learning approaches (in particular neural ordinary differential equations) has been used to model lumped dynamic systems such as electronic circuits automatically from data. In this work, we examine how modal decomposition can be combined with neural ordinary differential equations for modelling distributed musical systems. The proposed model leverages the analytical solution for linear vibration of system’s modes and employs a neural network to account for nonlinear dynamic behaviour. Physical parameters of a system remain easily accessible after the training without the need for a parameter encoder in the network architecture. As an initial proof of concept, we generate synthetic data for a nonlinear transverse string and show that the model can be trained to reproduce the nonlinear dynamics of the system. Sound examples are presented.

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Given the speedy computation of the FFT in current computer hardware, there are new possibilities for examining transformations for very long sounds. A zero-phase version of any audio signal can be obtained by zeroing the phase angle of its complex spectrum and taking the inverse FFT. This paper recommends additional processing steps, including zero-padding, transient suppression at the signal’s start and end, and gain compensation, to enhance the resulting sound quality. As a result, a sound with the same spectral characteristics as the original one, but with different temporal events, is obtained. Repeating rhythm patterns are retained, however. Zero-phase sounds are palindromic in the sense that they are symmetric in time. A comparison of the zero-phase conversion to the autocorrelation function helps to understand its properties, such as why the rhythm of the original sound is emphasized. It is also argued that the zero-phase signal has the same autocorrelation function as the original sound. One exciting variation of the method is to apply the method separately to the real and imaginary parts of the spectrum to produce a stereo effect. A frame-based technique enables the use of the zero-phase conversion in real-time audio processing. The zero-phase conversion is another member of the giant FFT toolset, allowing the modification of sampled sounds, such as drum loops or entire songs.

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