Hard Sync Without Aliasing

Hard sync”, a form of oscillator synchronization, is a technique which synthesizes a characteristic rich family of sounds. We describe how to perform it by integrating a bandlimited impulse pattern, avoiding the unpleasant aliasing heard in a naive digital rendering. The synthesis is refined by using a minimum-phase bandlimited step function, which eliminates lookahead and integration. This idea also gives simple bandlimited syntheses of other discontinuous waveforms. 1 What is hard sync? Oscillator synchronization involves two oscillators, a master and a slave, with frequencies f0 and f1. We will consider sawtooth oscillators. In hard sync, whenever the master cycles around, it resets the phase of the slave oscillator. The fundamental frequency of the slave’s output, is thus equal to f0. Figure 1 shows this for a master wavelength of 10 and a slave wavelength of 3. We treat the signal as unipolar, 0 to 1, for simplicity.