Pultec EQP-1A Modeling with Wave Digital Filters

This thesis presents the development of a virtual analog model of the passive equal-izer section of the Pultec EQP-1A studio equalizer using Wave Digital Filters (WDF). The aim of the project was to provide an accurate and high performance open-source emulation of the circuitry and sound characteristics of the original hardware unit. The development process involved compiling the original unit’s schematics, gener-ating LTSpice simulations, and implementing the circuit in Python using the pywdf library and R-Type adaptors (a kind of adaptor used for modeling complex circuit junctions that cannot be classified as series or parallel). Since the R-Type adaptors greatly affected the performance of the model, the circuit was slightly modified to maintain its behavior without the need for R-Type adaptors. The frequency response of the Python prototype was compared to the LTSpice simulation showing that at sufficiently high sampling rates the error between the model and the simulations are minimal. The Python model was then ported to C++ using the JUCE framework and Chowdsp’s wdf library to generate a VST3 plug-in that can be loaded into digital audio worksta-tions. The plug-in has oversampling capabilities to preserve the adequate behavior of the circuit at frequencies close to Nyquist. The performance and accuracy of the Python model was measured, and the C++ im-plementation compared against another open-source implementation of the circuit using WDFs and R-Type adaptors (developed in the Faust programming language). The final EQP-1A Python model was 75% faster than our own one that used R-Type adaptors and the C++ implementation was 40% faster than the EQP-1A implemen-tation in Faust and a much more accurate emulation of the original circuit

Music Production Behaviour Modelling

The new millennium has seen an explosion of computational approaches to the study of music production, due in part to the decreasing cost of computation and the increase of digital music production techniques. The rise of digital recording equipment, MIDI, digital audio workstations (DAWs), and software plugins for audio effects led to the digital capture of various processes in music production. This discretization of traditionally analogue methods allowed for the development of intelligent music production, which uses machine learning to numerically characterize and automate portions of the music production process. One algorithm from the field referred to as ``reverse engineering a multitrack mix'' can recover the audio effects processing used to transform a multitrack recording into a mixdown in the absence of information about how the mixdown was achieved. This thesis improves on this method of reverse engineering a mix by leveraging recent advancements in machine learning for audio. Using the differentiable digital signal processing paradigm, greybox modules for gain, panning, equalisation, artificial reverberation, memoryless waveshaping distortion, and dynamic range compression are presented. These modules are then connected in a mixing chain and are optimized to learn the effects used in a given mixdown. Both objective and perceptual metrics are presented to measure the performance of these various modules in isolation and within a full mixing chain. Ultimately a fully differentiable mixing chain is presented that outperforms previously proposed methods to reverse engineer a mix. Directions for future work are proposed to improve characterization of multitrack mixing behaviours