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Discrete-time synthesis of the sawtooth waveform with reduced aliasing

An efficient signal processing algorithm for generating a sawtooth waveform is proposed. The algorithm improves the trivial waveform sampling method, which suffers from low sound quality due to aliasing. The basic version of the new algorithm differentiates a piecewise parabolic waveform. Another version of the algorithm oversamples and decimates the parabolic wave with a simple filter prior to differentiation. The two algorithm variants improve the signal-to-noise ratio (SNR) over the trivial method by 10 and 15 dB, respectively. A perceptually weighted SNR suggests a larger subjective improvement. The proposed methods are applicable in a digital signal processor (DSP) implementation of subtractive sound synthesis.