![]() ![]() It is also interesting to note that many affine parameters seem highly correlated, whilst a few appear to move independently, suggesting that some NEWTs may work together to produce cohesive aspects of the signal, whilst others take momentary individual responsibility for signal components. This tells us that it has learnt to continuously shift and scale the input to the shaper functions, and also scale the output, whilst leaving the DC offset of the output signal almost untouched. However, \(\beta_N\) is barely varied at all. The model clearly makes use of \(\alpha_a\), \(\beta_a\), and \(\alpha_N\), varying many of these parameters widely across the length of the audio clip. In particular, the NEWT learns an implicit neural representation 3 of the shaping function \(f\) using a sinusoidal multi-layer perceptron (MLP).Īnd it turns out that we can get good results using tiny MLPs to represent our shaping functions – only 169 parameters each!Īffine transform parameters generated by the NEWT to synthesise audio Instead of manually designing our shaping function \(f\), however, the NEWT learns it from unlabelled audio. The NEWT is a neural network structure that performs waveshaping on an exciter signal. ![]() Or are we? NEWT: the neural waveshaping uni t This means if we want to model the temporal evolution of a specific target timbre, we’re out of luck! In Marc Le Brun’s original formulation 2, the function is defined as a sum of Chebyshev polynomials of the first kind, giving a precise combination of harmonics when \(a=1\).Īs we know, the balance of harmonics also varies, but with the Chebyshev polynomial design method we have no control over this variation. Putting all this together, we can define a simple waveshaping synthesiser:Īs you might have guessed, the tricky part here is choosing the function \(f\). We also introduce the normalising coefficient \(N\) which allows us to vary the timbre separately from the amplitude of the final signal. We do this using the distortion index \(a\). If we want to vary the timbre over time, we can change the amplitude of the signal we pass into \(f\). With this knowledge, we can produce a steady signal consisting of multiple harmonics. This means when \(y\) is purely harmonic, \(f(y)\) will be too. In brief, we take a simple sinusoid, \(\cos\omega n\), and we pass it through a nonlinear function, which produces a sum of harmonics of that sinusoid: Many audio synthesis methods focus on producing such harmonics, and waveshaping synthesis 2 is one of these approaches. In other words, it consists of multiple components oscillating at integer multiples of a single fundamental frequency, called harmonics. ![]() Musical audio often has a harmonic structure. This page is a supplement to our paper, accepted for publication at ISMIR 2021. Our approach adds to the growing family of differentiable digital signal processing (DDSP) 1 methods by learning waveshaping functions with neural networks. We’re excited to present our work on Neural Waveshaping Synthesis, a method for efficiently synthesising audio waveforms with neural networks. By Ben Hayes, Charalampos Saitis, György Fazekas ![]()
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