Fast Additive Sound Synthesis Using Polynomials

This paper presents a new fast sound synthesis method using polynomials. This is an additive method, where polynomials are used to approximate sine functions. Traditional additive synthesis requires each sample to be generated for each partial oscillator. Then all these partial samples are summed up to obtain the resulting sound sample, thus making the synthesis time proportional to the product of the number of oscillators and the sampling rate. By using polynomial approximations, we instead sum up only the oscillator coefficients and then generate directly the sound sample from these new coefficients. Most of computation time is consumed by a data structure that manages the update of the generator coefficients as a priority queue. Practical implementations show that Polynomial Additive Sound Synthesis (PASS) is particularly efficient for low-frequency signals.