This paper explores Frequency Modulation (FM) for use in music synthesis. We take an in-depth look at Linear FM, LinearThrough-Zero FM, Phase Modulation (PM) and Exponential FM, and discuss their pros and cons for sound synthesis in a digital system. In the process we derive some useful formulas and discuss their implementation details. In particular we derive analytic expressions for DC correcting Exponential FM, and make it match the modulation depth of Linear FM. Finally, we review practical antialiasing solutions.

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