UTSA Electronic Music Studio Web Site: FM Synthesis

FREQUENCY MODULATION (John Chowning)

The fact that the temporal evolution of the frequency components of the spectrum can be easily controlled is perhaps the most striking attribute of the technique.

FM: The instantaneous frequency of a carrier wave is varied according to a modulator wave such that the rate at which the carrier varies is the rate of the modulating wave, or modulating frequency. It results from applying an output from the modulator to the control voltage input of the carrier.

Peak deviation: the amount the carrier varies around its average. This is directly proportional to the amplitude of the modulator wave.

Parameters:
- c: carrier or average frequency
- m: modulating frequency
- d: peak deviation
Modulation index: the modulation index measures the peak deviation of the carrier from its average. It is expressed as the ratio i = d/m. (mod. index = peak deviation/modulation freq.)

Sidebands: Sidebands occur in pairs and result from the relationship of c\m when the modulating frequency is above 32hz. The formula for obtaining these is c +/- n m. (n = 0,1,2,3..... Below 32hz results in vibrato effects.

Reflected sideband frequencies: The special richness of FM lies in the fact that there are ratios of c and m and values of the index that can produce sideband components which fall into the negative domain of the spectrum. The negative components reflect from 0hz and mix with the components in the positive domain. The variety of frequency relations which result includes harmonic (if c/m have common divisors) and inharmonic spectra (if c/m involves irrational numbers). These reflected sideband frequencies recieve an inversion of phase when sent back into the positive domain.

Bessel functions: the amplitudes of the carrier and sideband components are determined by Bessel functions. Each sideband pair has its own Bessel function.