Abstract
Discretetime modelling strategies of analogue Moog sawtooth oscillator waveforms are presented. Two
alternative approaches suitable for realtime 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
firstorder IIR postequalising 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 postequalising
the fourthorder Bspline bandlimited step function sawtooth oscillator.
Files
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)
Frequency 
98.10 Hz 
220.62 Hz 
495.44 Hz 
1.049 kHz 
2.096 kHz 
6.256 kHz 
Recording 
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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 resetcorrected
model of Kleimola et al., 2010, reference [19] in the manuscript.
Postequalised 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.
