Download Barberpole Phasing and Flanging Illusions Various ways to implement infinitely rising or falling spectral notches, also known as the barberpole phaser and flanging illusions, are described and studied. The first method is inspired by the Shepard-Risset illusion, and is based on a series of several cascaded notch filters moving in frequency one octave apart from each other. The second method, called a synchronized dual flanger, realizes the desired effect in an innovative and economic way using two cascaded time-varying comb filters and cross-fading between them. The third method is based on the use of single-sideband modulation, also known as frequency shifting. The proposed techniques effectively reproduce the illusion of endlessly moving spectral notches, particularly at slow modulation speeds and for input signals with a rich frequency spectrum. These effects can be programmed in real time and implemented as part of a digital audio processing system.
Download Time-Variant Gray-Box Modeling of a Phaser Pedal A method to measure the response of a linear time-variant (LTV) audio system is presented. The proposed method uses a series of short chirps generated as the impulse response of several cascaded allpass filters. This test signal can measure the characteristics of an LTV system as a function of time. Results obtained from testing of this method on a guitar phaser pedal are presented. A proof of concept gray-box model of the measured system is produced based on partial knowledge about the internal structure of the pedal and on the spectral analysis of the measured responses. The temporal behavior of the digital model is shown to be very similar to that of the measured device. This demonstrates that it is possible to measure LTV analog audio systems and produce approximate virtual analog models based on these results.
Download Rounding Corners with BLAMP The use of the bandlimited ramp (BLAMP) function as an antialiasing tool for audio signals with sharp corners is presented. Discontinuities in the waveform of a signal or its derivatives require infinite bandwidth and are major sources of aliasing in the digital domain. A polynomial correction function is modeled after the ideal BLAMP function. This correction function can be used to treat aliasing caused by sharp edges or corners which translate into discontinuities in the first derivative of a signal. Four examples of cases where these discontinuities appear are discussed: synthesis of triangular waveforms, hard clipping, and half-wave and fullwave rectification. Results obtained show that the BLAMP function is a more efficient tool for alias reduction than oversampling. The polynomial BLAMP can reduce the level of aliasing components by up to 50 dB and improve the overall signal-to-noise ratio by about 20 dB. The proposed method can be incorporated into virtual analog models of musical systems.
Download Virtual Analog Buchla 259 Wavefolder An antialiased digital model of the wavefolding circuit inside the Buchla 259 Complex Waveform Generator is presented. Wavefolding 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 nonlinear 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.
Download Creating Endless Sounds This paper proposes signal processing methods to extend a stationary part of an audio signal endlessly. A frequent occasion is that there is not enough audio material to build a synthesizer, but an example sound must be extended or modified for more variability. Filtering of a white noise signal with a filter designed based on high-order linear prediction or concatenation of the example signal can produce convincing arbitrarily long sounds, such as ambient noise or musical tones, and can be interpreted as a spectral freeze technique without looping. It is shown that the random input signal will pump energy to the narrow resonances of the filter so that lively and realistic variations in the sound are generated. For realtime implementation, this paper proposes to replace white noise with velvet noise, as this reduces the number of operations by 90% or more, with respect to standard convolution, without affecting the sound quality, or by FFT convolution, which can be simplified to the randomization of spectral phase and only taking the inverse FFT. Examples of producing endless airplane cabin noise and piano tones based on a short example recording are studied. The proposed methods lead to a new way to generate audio material for music, films, and gaming.
Download Waveshaping with Norton Amplifiers: Modeling the Serge Triple Waveshaper The Serge Triple Waveshaper (TWS) is a synthesizer module designed in 1973 by Serge Tcherepnin, founder of Serge Modular Music Systems. It contains three identical waveshaping circuits that can be used to convert sawtooth waveforms into sine waves. However, its sonic capabilities extend well beyond this particular application. Each processing section in the Serge TWS is built around what is known as a Norton amplifier. These devices, unlike traditional operational amplifiers, operate on a current differencing principle and are featured in a handful of iconic musical circuits. This work provides an overview of Norton amplifiers within the context of virtual analog modeling and presents a digital model of the Serge TWS based on an analysis of the original circuit. Results obtained show the proposed model closely emulates the salient features of the original device and can be used to generate the complex waveforms that characterize “West Coast” synthesis.
Download Modelling of nonlinear state-space systems using a deep neural network In this paper we present a new method for the pseudo black-box modelling of general continuous-time state-space systems using a discrete-time state-space system with an embedded deep neural network. Examples are given of how this method can be applied to a number of common nonlinear electronic circuits used in music technology, namely two kinds of diode-based guitar distortion circuits and the lowpass filter of the Korg MS-20 synthesizer.
Download Differentiable IIR Filters for Machine Learning Applications In this paper we present an approach to using traditional digital IIR
filter structures inside deep-learning networks trained using backpropagation. We establish the link between such structures and
recurrent neural networks. Three different differentiable IIR filter
topologies are presented and compared against each other and an
established baseline. Additionally, a simple Wiener-Hammerstein
model using differentiable IIRs as its filtering component is presented and trained on a guitar signal played through a Boss DS-1
guitar pedal.
Download Differentiable White-Box Virtual Analog Modeling Component-wise circuit modeling, also known as “white-box”
modeling, is a well established and much discussed technique in
virtual analog modeling. This approach is generally limited in accuracy by lack of access to the exact component values present in
a real example of the circuit. In this paper we show how this problem can be addressed by implementing the white-box model in a
differentiable form, and allowing approximate component values
to be learned from raw input–output audio measured from a real
device.
Download A Virtual Analog Model of the Edp Wasp VCF In this paper we present a virtual analog model of the voltagecontrolled filter used in the EDP Wasp synthesizer. This circuit is an interesting case study for virtual analog modeling due to its characteristic nonlinear and highly dynamic behavior which can be attributed to its unusual design. The Wasp filter consists of a state variable filter topology implemented using operational transconductance amplifiers (OTAs) as the cutoff-control elements and CMOS inverters in lieu of operational amplifiers, all powered by a unipolar power supply. In order to accurately model the behavior of the circuit we propose extended models for its nonlinear components, focusing particularly on the OTAs. The proposed component models are used inside a white-box circuit modeling framework to create a digital simulation of the filter which retains the interesting characteristics of the original device.