Synthesis of audio spectra using a diffraction model

Abstract

It is shown that the intensity variations of an audio signal in the frequency domain can be obtained by using a mathematical function containing a series of weighted complex Bessel functions. With proper choice of values for two parameters, this function can transform an input spectrum of discrete frequencies of unit intensity into the known spectra of different musical instruments. Specific examples of musical instruments are considered for evaluating the performance of this method. It is found that this function yields musical spectra with a good degree of accuracy.