Digital FM Synthesis

In the most simple form, FM digital synthesis consists of two sine waves. One is called the modulating wave and the other is called the carrier wave. The carrier wave is the only waveform that is audible. The modulating wave does just as it sounds, it modulates the amplitude of the carrier wave, and acts as a control value. The frequency of the modulating frequency controls the rate of change in the carrier wave; it controls how fast the modulation occurs in the carrier wave. And the amplitude of the modulating frequency controls the degree of change in the carrier frequency. In addition there is the modulation index, which is the ratio of the largest frequency in the spread to the frequency of the modulation frequency. The modulation index tells you how severe the modulation of the carrier frequency is. Next are sidebands. They are much like alias frequencies, where they are frequencies created above and below the carrier frequency. Sidebands are calculated with the ratio C:M, where C is the carrier frequency and M is the modulating frequency. This ratio determines the spacing between the frequencies (partials). Depending on the ratio (C:M), there are only three basic relationships of partials; integer, slightly detuned, and non-integer. Integers are simple ratios that create harmonic structures. They are frequencies at exact multiples of the fundamental frequency, which would be the carrier frequency. Slightly detuned integers also make the same idea of exact multiples from the carrier, but since they are “detuned”, it means that they will continually be further and further from the exact multiple as the harmonics get further from the fundamental. This will become more evident, as they will become non-multipels of the fundamental, them more severe it gets. And what seems like the most obtrusive, non-integer “harmonics” are actually frequencies that don’t fall into any sort of pattern between the carrier and modulating frequencies. However, they are the most