Computational methods for real-time Fourier synthesis

In Fourier synthesis, natural musical sounds are produced by summing time-varying sinusoids. Sounds from individual instruments are analyzed to find the amplitude and frequency characteristics for their sinusoids; interpolation between the characteristics of several sounds is used to produce intermediate timbres. An ensemble can be synthesized by summing all the sinusoids for several sounds, but in practice it is difficult to perform such computations in real time. To solve this problem on inexpensive hardware, the author takes advantage of the masking effects of the auditory system. By avoiding the computations for perceptually unimportant sinusoids, and by using other computation reduction techniques to achieve interpolation, a large ensemble can be synthesized in real time. Unlike existing computation reduction techniques, the techniques described in this correspondence do not sacrifice independent fine control over the amplitude and frequency characteristics of each sinusoid