Discrete-Time Modelling of the Moog Sawtooth Oscillator Waveform

Abstract

Discrete-time modelling strategies of analogue Moog sawtooth oscillator waveforms are presented. Two alternative approaches suitable for real-time implementation are proposed, one modelling the analogue waveform in time domain using phase distortion synthesis and another matching the spectrum of an existing antialiasing sawtooth oscillator to the corresponding analogue spectrum using a first-order IIR post-equalising filter. A parameter estimation procedure for both approaches is explained and performed. Performance evaluation using polynomial fits for the estimated parameters is carried out, and good matches between the model outputs and recorded waveforms are obtained. The best match of the tested algorithms is produced by the phase distortion model and by post-equalising the fourth-order B-spline bandlimited step function sawtooth oscillator.

Audibility of aliasing distortion in sawtooth signals and its implications for oscillator algorithm design

“…Digital emulation of the subtractive sound synthesis principle has later become a topic of interest. [3][4][5][6] One branch of this research concentrates on digital models of analog filters 5,7-9 but most of the research efforts have focused on oscillator algorithms. [10][11][12] Trivial sampling of the continuous-time sawtooth waveform results in aliasing distortion, which is caused by discontinuities in the waveform.…”

“…11,[13][14][15] Oscillator algorithms reducing the aliasing distortion in digitally generated classical waveforms have been extensively developed. 6,[16][17][18] Some of these algorithms remove the aliasing distortion completely 15,[19][20][21][22] but there are also approaches that allow some aliasing. 4,16,18,22 In the latter case, the level of the aliased component is lower than in the trivially generated waveform.…”