ThesisPDF Available

System Identification of Nonlinear Audio Circuits

Authors:
  • Nektar Technology Inc.

Abstract and Figures

Digital systems gain more and more popularity in todays music industry. Musicians and producers are using digital systems because of their advantages over analog electronics. They require less physical space, are cheaper to produce and are not prone to aging circuit components or temperature variations. Furthermore, they always produce the same output signal for a defined input sequence. However, musicians like vintage equipment. Old guitar amplifiers or legendary recording equipment are sold at very high prices. Therefore, it is desirable to create digital models of analog music electronics which can be used in modern digital environments. This work presents an approach for recreating nonlinear audio circuits using system identification techniques. Measurements of the input- and output-signals from the analog reference devices are used to adjust a digital model treating the reference device as a ‘black-box’. With this technique the schematic of the reference device does not need to be known and no circuit elements have to be measured to recreate the analog device. An appropriate block-based model is chosen, depending on the type of reference system. Then the parameters of the digital model are adjusted with an optimization method according to the measured input- and output-signals. The performance of the optimized digital model is evaluated with objective scores and listening tests. Two types of nonlinear reference systems are examined in this work. The first type of reference systems are dynamic range compressors like the ‘MXR Dynacomp’, the ‘Aguilar TLC’, or the ‘UREI 1176LN’. A block-based model describing a generic dynamic range compression system is chosen and an automated routine is developed to adjust it. The adapted digital models are evaluated with objective scores and a listening test is performed for the UREI 1176LN studio compressor. The second type of nonlinear systems are distortion systems like e.g. amplifiers for electric guitars. This work presents novel modeling approaches for different kinds of distortion systems from basic distortion circuits which can be found in distortion pedals for guitars to (vintage) guitar amplifiers like the ‘Marshall JCM900’, or the ‘Fender Bassman’. The linear blocks of the digital model are measured and used in the model while the nonlinear blocks are adapted with parameter optimization methods like the Levenberg–Marquardt method. The quality of the adjusted models is evaluated with objective scores and listening tests. The adjusted digital models give convincing results and can be implemented as real-time digital versions of their analog counterparts. This enables the musician to safe a snapshot of a certain sound and recall it anytime with a digital system like a VST plug-in or as a program on a dedicated hardware.
Content may be subject to copyright.
A preview of the PDF is not available
... Methods of the second type exploit machine learning or system identification [3][4][5][6][7][8][9][10][11][12]. Using pairs of clean input and distorted output sounds of the target device, the mapping from the input to output is acquired. ...
... Methods of the second type are further classified into two subgroups. Those in the first subgroup are called block-oriented models [3][4][5][6][7]. Electronic circuits in the device typically consist of a linear filtering block followed by a nonlinear clipping block. ...
Article
The present paper proposes a distortion pedal modeling method using the so-called WaveNet. A state-of-the-art method constructs a feedforward network by modifying the original autoregressive WaveNet, and trains it so that a loss function defined by the normalized mean squared error between the high-pass filtered outputs is minimized. This method works well for pedals with low distortion, but not for those with high distortion. To solve this problem, the proposed method exploits the same WaveNet, but a novel loss function, which is defined by a weighted sum of errors in time and time-frequency (T-F) domains. The error in the time domain is defined by the mean squared error without the high-pass filtering, while that in the T-F domain is defined by a divergence between spectral features computed from the short-time Fourier transform. Numerical experiments using a pedal with high distortion, the Ibanez SD9, show that the proposed method is capable of precisely reproducing high-frequency components without attenuation of low-frequency components compared to the state-of-the-art method.
Conference Paper
Full-text available
An antialiased digital model of the wavefolding circuit inside the Buchla 259 Complex Waveform Generator is presented. Wave-folding is a type of nonlinear waveshaping used to generate complex harmonically-rich sounds from simple periodic waveforms. Unlike other analog wavefolder designs, Buchla's design features five op-amp-based folding stages arranged in parallel alongside a direct signal path. The nonlinear behavior of the system is accurately modeled in the digital domain using memoryless mappings of the input-output voltage relationships inside the circuit. We pay special attention to suppressing the aliasing introduced by the non-linear frequency-expanding behavior of the wavefolder. For this, we propose using the bandlimited ramp (BLAMP) method with eight times oversampling. Results obtained are validated against SPICE simulations and a highly oversampled digital model. The proposed virtual analog wavefolder retains the salient features of the original circuit and is applicable to digital sound synthesis.
Thesis
Full-text available
Nonlinear systems identification and modeling is a central topic in many engineering areas since most real world devices may exhibit a nonlinear behavior. This thesis is devoted to the emulation of the nonlinear devices present in a guitar signal chain. The emulation aims to replace the hardware elements of the guitar signal chain in order to reduce its cost, its size, its weight and to increase its versatility. The challenge consists in enabling an accurate nonlinear emulation of the guitar signal chain while keeping the execution time of the model under the real time constraint. To do so, we have developed two methods. The first method developed in this thesis is based on a subclass of the Volterra series where only static nonlinearities are considered: the polynomial parallel cascade of Hammerstein models. The resulting method is called the Hammerstein Kernels Identification by Sine Sweep method (HKISS). According to the tests carried out in this thesis and to the results obtained, the method enables an accurate emulation of nonlinear audio devices unless if the system to model is too far from an ideal Hammerstein one. The second method, based on neural networks, better generalizes to guitar signals and is well adapted to the emulation of guitar signal chain (e.g., tube and transistor amplifiers). We developed and compared eight models using different performance indexes including listening tests. The accuracy obtained depends on the tested audio device and on the selected model but we have shown that the probability for a listener to be able to hear a difference between the target and the prediction could be less than 1%. This method could still be improved by training the neural networks with an objective function that better corresponds to the objective of this audio application, i.e., minimizing the audible difference between the target and the prediction. Finally, it is shown that these two methods enable an accurate emulation of a guitar signal chain while keeping a fast execution time which is required for real-time audio applications.
Conference Paper
Full-text available
This paper proposes to use a recurrent neural network for black-box modelling of nonlinear audio systems, such as tube amplifiers and distortion pedals. As a recurrent unit structure, we test both Long Short-Term Memory and a Gated Recurrent Unit. We compare the proposed neural network with a WaveNet-style deep neural network, which has been suggested previously for tube amplifier modelling. The neural networks are trained with several minutes of guitar and bass recordings, which have been passed through the devices to be modelled. A real-time audio plugin implementing the proposed networks has been developed in the JUCE framework. It is shown that the recurrent neural networks achieve similar accuracy to the WaveNet model, while requiring significantly less processing power to run. The Long Short-Term Memory recurrent unit is also found to outperform the Gated Recurrent Unit overall. The proposed neural network is an important step forward in computationally efficient yet accurate emulation of tube amplifiers and distortion pedals.
Chapter
Full-text available
Valve amplifiers have been modulated recently by digital signal processing techniques, using the Wiener-Hammerstein cell. The key of this approach is to identify the non-linear static transfer function. In the present contribution we model audio distortion pedal effects and propose a transfer function model derived from a modification of the Shockley equation. Six limiter circuits with different types of diodes (silicon, germanium and LED) were evaluated using a voltage sine wave of 10 Hz and amplitude such as to provide a 10 mA input current. Ten seconds of input and output signals were sampled (100 kSamples/s) and the model was fitted to the data using the Levenberg-Marquardt non-linear least square method. The model worked well, providing a root mean square standard error between the data and best fit less than 10⁻⁴, except for the LED limiter circuit. The present approach resulted in an analytical representation of the non-linear transfer function, which can generate directly from a discretised input signal the corresponding output signal according to a desired response of a chosen limiter model.
Article
Full-text available
An assessment of filters for classic oversampled audio waveshaping schemes is carried out in this paper, pursuing aliasing reduction. For this purpose, the quality measure of the A-weighted noise-to-mask ratio is computed for test tones covering the frequency range from 27.5 Hz to 4.186 kHz, sampled at 44.1 kHz, and processed at eight-times oversampling. All filters are designed to have their passband contained within a ±1 dB range and to display a minimum stopband attenuation value of 40 dB.Waveshaping of sinusoids via hard clipping is investigated: the spectral enrichment due to the discontinuities introduced by its nonlinear transfer function maximizes aliasing distortion. The obtained results suggest that linear interpolation equalized with a high shelving filter is a sufficiently good method for upsampling. Concerning decimation, the interpolated FIR, elliptic, and cascaded integrator-comb filters all improve the results with respect to the trivial case. Regarding performance, the cascaded integrator-comb filter is the only tested decimation filter that achieves perceptually sufficient aliasing suppression for the entire frequency range when combined with the linear interpolator.
Conference Paper
Full-text available
The purpose of this paper is to give theoretical and practical advice to DSP programmers willing to implement efficient real-time circuit simulation algorithms. It summarizes the fundamental concepts behind the most widespread circuit modeling techniques and gives the reader sufficient references to get started. Then it tackles on a certain number of topics that are often neglected in theoretical studies yet highly relevant in real-world applications. Hopefully, this paper might also serve as a reference and an invite for researchers to direct their efforts towards problems and solutions that have a concrete impact.
Article
Traditional measurement of multimedia systems, e.g. linear impulse response and transfer function, are sufficient but not faultless. For these methods the pure linear system is considered and nonlinearities, which are usually included in real systems, are disregarded. One of the ways to describe and analyze a nonlinear system is by using Volterra Series representation. However, this representation uses an enormous number of coefficients. In this work a simplification of this method is proposed and an experiment with an audio amplifier is shown.
Conference Paper
Analog audio effects and synthesizers often owe their distinct sound to circuit nonlinearities. Faithfully modeling such significant aspect of the original sound in virtual analog software can prove challenging. The current work proposes a generic data-driven approach to virtual analog modeling and applies it to the Fender Bassman 56F-A vacuum-tube amplifier. Specifically, a feedforward variant of the WaveNet deep neural network is trained to carry out a regression on audio waveform samples from input to output of a SPICE model of the tube amplifier. The output signals are pre-emphasized to assist the model at learning the high-frequency content. The results of a listening test suggest that the proposed model accurately emulates the reference device. In particular, the model responds to user control changes, and faithfully restitutes the range of sonic characteristics found across the configurations of the original device.