New Perspectives on Distortion Synthesis for Virtual Analog Oscillators

The term “virtual analog” (VA) first appeared in the 1990s with the commercial introduction of digital synthesizer instruments that were intended to emulate the earlier analog subtractive synthesizers, such as those produced by, among others, Moog or Sequential Circuits (Smith 2008). In creating a “virtual analog” digital model, two approaches are possible: the first is to build an explicit digital model derived from the various electrical components that form the original analog circuit; the second is to use digital processing structures that will produce outputs that mimic those of the analog system. To date, the second approach has been used for the implementation of the elements of virtual analog subtractive synthesizers, as real-time computational constraints limit the efficacy of circuit models in usable software instruments (Civolani and Fontana 2008). Among the features of a subtractive synthesis system, one aspect that has received more attention than others is algorithms for real-time digital generation of the periodic waveforms associated with voltage-controlled oscillators (VCO), such as sawtooths, square waves, and triangle waves, also known as the classic analog waveforms (Stilson 2006). Although the original analog waveforms theoretically had an infinite bandwidth, the digital versions must be bandlimited to half the sampling frequency (Stilson 2006). If this is not the case, the audio output can exhibit excessive aliasing distortion, which can severely corrupt the sound quality. This distortion is manifested as audio disturbances that include inharmonicity, beating, and heterodyning. It can be particularly severe when the ratio of the waveform fundamental frequency to the sampling frequency is not an integer, as the aliased components will then fall in between the signal harmonics (Välimäki and