Alias-Free Digital Synthesis of Classic Analog Waveforms

Techniques are reviewed and presented for alias-free digital synthesis of classical analog synthesizer waveforms such as pulse train and sawtooth waves. Techniques described include summation of bandlimited primitive waveforms as well as table-lookup techniques. Bandlimited pulse and triangle waveforms are obtained by integrating the difference of two out-of-phase bandlimited impulse trains. Bandlimited impulse trains are generated as a superposition of windowed sinc functions. Methods for more general bandlimited waveform synthesis are also reviewed. Methods are evaluated from the perspectives of sound quality, computational economy, and ease of control.