Frequency modulation synthesis of musical instruments has been studied for years and its limitations are well known. By modifying the basic closed-form equations to work in the complex domain, an alternative method that can overcome some of these limitations is presented. The proposed approach provides a smoothly evolving spectrum with regard to variations in modulation index. A phase-synchronous version is discussed with application to resonant and formant synthesis. A comparison with the classical frequency modulation approach illustrates its advantages. Adaptive applications of the algorithm are introduced and explored.
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