Sinusoidal Synthesis Method using a Force-based Algorithm

In this paper we propose a synthesis method using a force-based algorithm to control frequencies of multiple sine waves. In order to implement this synthesis method, we analyze an existing sound source using a fast Fourier transform (FFT). Spectral peaks which have large magnitudes are regarded as heavy partials and assigned large attractive forces. A few hundred sine waves with stationary amplitudes are placed in a frequency space on which forces generated in the analysis phase are applied. The frequencies of the partials gravitate to the nearest peak of the reference spectrum from the source sound. As more sine waves are combined at the large peaks, the sound synthesized by the partials gradually transforms into the reference spectrum. In order to prevent the frequencies of the partials from gravitating onto localized peaks, each partial is assigned a repulsive force against all others. Through successful control of these attractive and repulsive forces, roughness and speed variation of the synthesis can be achieved. Moreover, by increasing or decreasing the number of partials according to the total amplitude of the source sound, amplitude envelope following is achieved.