Efficient Synthesis of Piano Tones with Damped Bessel Functions

In this paper a novel technique for efficient synthesis of waveforms generated by musical instruments is presented. This methodology represents single tones produced by musical instruments as a series of orthogonal Bessel functions, similarly to an additive synthesis that, instead, uses sinusoidal partials. Bessel functions possess a pitch that slowly varies with time, and are thus suited to model musical tones that usually exhibit similar characteristics. A comparative listening test has been performed, and the synthetically created piano sounds have been compared to those generated by traditional additive synthesis. Bessel-based synthesis generally achieved a higher score than the sinusoidal-based approach. The limited amount of memory resources used makes this technique suitable to be implemented on a digital signal processor.