A signal flow diagram describing simple frequency modulation (FM) with sinusoidal oscillators is shown in Fig. 9.
A signal flow diagram for simple FM synthesis.
The carrier oscillator ``center frequency'' is fc and its amplitude is Ac.
The modulating oscillator has frequency fm and amplitude . Note that controls the peak frequency deviation.
The instantaneous frequency value applied to the carrier oscillator frequency input is given by
When , no modulation takes place. As increases, the deviation of the carrier frequency (fc) increases.
Using sinusoidal waveforms for both the carrier and modulator, this modulation produces additional spectral components in the output signal at multiples of , where k is an integer, as sketched in Fig.10.
The spectrum of a simple sinusoidal FM synthesis.
Note the inherent nonlinearity of this operation ... ``frequencies come out that didn't go in''.
The spectral components are spaced equally apart at intervals of fm (in the absence of fold-over).
Increasing increases the energy in the sidebands at the expense of energy at the carrier frequency.
The Max/MSP patch fm.maxpat, shown below, demonstrates FM modulation.
The Matlab script FM.m
provides an aural and visual demonstration of the modulator's affect on the resulting FM spectrum.