A fixed-point recursive digital oscillator for additive synthesis of audio

This paper summarizes our work adapting a recursive digital resonator for use on sixteen-bit fixed-point hardware. Our modified oscillator is a two-pole filter that maintains frequency precision at a cost of two additional operations per filter sample. The new filter´s error properties are expressly matched to use in the range of frequencies relevant to additive synthesis of digital audio and sinusoidal modelling of speech in order to minimize the additional computational overhead. We present the algorithm, an error analysis, a performance analysis, and measurements of an implementation on a fixed-point vector microprocessor system