A naive digital sawtooth resets only on sample boundaries, causing aliasing

Analog sawtooth oscillators discharge a capacitor continuously, at the exact instant a threshold is reached. A digital equivalent using a counter-accumulator can only reset on a sample boundary — not at the exact theoretical moment. This misalignment between the desired reset point and the nearest sample creates alias frequencies: spurious tones at wrong pitch positions. The article notes this “won’t give us adequate results without a very high sample rate,” which is why a simple counter cannot substitute for the analog original without additional technique (band-limiting or wavetable lookup). The artifact is most problematic at higher pitches where fewer samples fall within each cycle.

Examples

A 1 kHz sawtooth at 44.1 kHz sample rate has ~44 samples per cycle — the reset lands within one sample of the ideal point. At 10 kHz, only ~4.4 samples per cycle — the reset error is proportionally much larger and aliases are clearly audible.

Assessment

Explain why a simple counter-based digital sawtooth oscillator produces aliasing, and why the problem worsens at higher pitches. What would need to change to eliminate the artifact?