Download Fast Approximation of the Lambert W Function for Virtual Analog Modelling When modelling circuits one has often to deal with equations containing both a linear and an exponential part. If only a single exponential term is present or predominant, exact or approximate closed-form solutions can be found in terms of the Lambert W function. In this paper, we propose reformulating such expressions in terms of the Wright Omega function when specific conditions are met that are customary in practical cases of interest. This eliminates the need to compute an exponential term at audio rate. Moreover, we propose simple and real-time suitable approximations of the Omega function. We apply our approach to a static and a dynamic nonlinear system, obtaining digital models that have high accuracy, low computational cost, and are stable in all conditions, making the proposed method suitable for virtual analog modelling of circuits containing semiconductor devices.
Download A Digital Model of the Buchla Lowpass-Gate In recent years there has been an increasing amount of interest in the style of synthesis implemented by Don Buchla in his instrument designs from the early 1960s until the present. A key part of the Buchla synthesizer and its characteristic quality is the ’lowpass gate’ filter and the acoustic-like plucked sounds that it provides. In this work we examine the circuit of the low-pass gate, both its audio and control portions. We propose a number of digital models of these circuits, as well as a model of the photoresistive optoisolator or ’vactrol’ used within them. In the case of the audio path of the device, we pay particular attention to maintaining desirable behavior under time-variation of its parameters. The resulting digital model retains much of the interesting character of the analog system, and is computationally cheap enough to use within a standard computer-music setup.
Download Optimal Integer Order Approximation of Fractional Order Filters Fractional order filters have been studied since a long time,
along with their applications to many areas of physics and engineering. In particular, several solutions have been proposed in
order to approximate their frequency response with that of an ordinary filter. In this paper, we tackle this problem with a new approach: we solve analytically a simplified version of the problem
and we find the optimal placement of poles and zeros, giving a
mathematical proof and an error estimate. This solution shows improved performance compared to the current state of the art and is
suitable for real-time parametric control.
Download Antialiasing in BBD Chips Using BLEP Several methods exist in the literature to accurately simulate Bucket
Brigade Device (BBD) chips, which are widely used in analog
delay-based audio effects for their characteristic lo-fi sound, which
is affected by noise, nonlinearities and aliasing. The latter is a desired quality, being typical of those chips. However, when simulating BBDs in a discrete-time domain environment, additional aliasing components occur that need to be suppressed. In this work, we
propose a novel method that applies the Bandlimited Step (BLEP)
technique, effectively minimizing aliasing artifacts introduced by
the simulation. The paper provides some insights on the design
of a BBD simulation using interpolation at the input for clock rate
conversion and, most importantly, shows how BLEP can be effective in reducing unwanted aliasing artifacts. Interpolation is shown
to have minor importance in the reduction of spurious components.
Download Analysis and Emulation of Early Digitally-Controlled Oscillators Based on the Walsh-Hadamard Transform Early analog synthesizer designs are very popular nowadays, and the discrete-time emulation of voltage-controlled oscillator (VCO) circuits is covered by a large number of virtual analog (VA) textbooks, papers and tutorials. One of the issues of well-known VCOs is their tuning instability and sensitivity to environmental conditions. For this reason, digitally-controlled oscillators were later introduced to provide stable tuning. Up to now, such designs have gained much less attention in the music processing literature. In this paper, we examine one of such designs, which is based on the Walsh-Hadamard transform. The concept was employed in the ARP Pro Soloist and in the Welson Syntex, among others. Some historical background is provided, along with a discussion on the principle, the actual implementation and a band-limited virtual analog derivation.
Download A Quadric Surface Model of Vacuum Tubes for Virtual Analog Applications Despite the prevalence of modern audio technology, vacuum tube amplifiers continue to play a vital role in the music industry. For this reason, over the years, many different digital techniques have been introduced for accomplishing their emulation. In this paper, we propose a novel quadric surface model for tube simulations able to overcome the Cardarilli model in terms of efficiency whilst retaining comparable accuracy when grid current is negligible. After showing the model capability to well outline tubes starting from measurement data, we perform an efficiency comparison by implementing the considered tube models as nonlinear 3-port elements in the Wave Digital domain. We do this by taking into account the typical common-cathode gain stage employed in vacuum tube guitar amplifiers. The proposed model turns out to be characterized by a speedup of 4.6× with respect to the Cardarilli model, proving thus to be promising for real-time Virtual Analog applications.