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.
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  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.