Jussi Pekonen, Victor Lazzarini, Joseph Timoney, Jari Kleimola, and Vesa Välimäki

Discrete-Time Modelling of the Moog Sawtooth Oscillator Waveform

Companion page for a paper published in EURASIP Journal on Advances in Signal Processing, special issue in Musical Applications of Real-Time Signal Processing

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.

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Demos

In the following examples, the approach under investigation is given in the section heading, and the fundamental frequency of oscillation is given above the links to the sound files. A sampling frequency of 44.1 kHz is used in all sound files.

References (Recorded Moog Sawtooth Waveforms)

Phase Distortion Model

The term ‘polynomial’ refers to the approach where the polynomial approximation of the model parameter is used, and the term ‘tabular’ to the approach where the estimated parameter values are used, and the term ‘single’ to the approach where a constant model parameter is used at all frequencies. The term “SMC model” refers to the reset-corrected model of Kleimola et al., 2010, reference [19] in the manuscript.

Post-equalised Antialiasing Oscillator Algorithms

Here, the term ‘unfiltered’ refers to the output of the underlying oscillator itself, and the other terms refer to the same approaches as with the phase distortion model.