Basic Frequency Modulation

A signal flow diagram describing simple frequency modulation (FM) with sinusoidal oscillators is shown in Fig. 9.

Figure 9: A signal flow diagram for simple FM synthesis.
$\begin{figure}\begin{center} \epsfig{file=figures/fmblock.eps, width=1.5in} \end{center} \end{figure}$
The carrier oscillator “center frequency” is and its amplitude is .
The modulating oscillator has frequency and amplitude $\Delta f$ . Note that $\Delta f$ controls the peak frequency deviation.
The instantaneous frequency value applied to the carrier oscillator frequency input is given by

$\displaystyle f(t) = f_c + \Delta f \sin(2 \pi f_m t)$
When $\Delta f = 0$ , no modulation takes place. As $\Delta f$ increases, the deviation of the carrier frequency () increases.
Using sinusoidal waveforms for both the carrier and modulator, this modulation produces additional spectral components in the output signal at multiples of $f_c \pm k f_m$ , where is an integer, as sketched in Fig.10.

Figure 10: The spectrum of a simple sinusoidal FM synthesis.
$\begin{figure}\begin{center} \epsfig{file=figures/fmspectrum.eps, width=3.0in} \end{center} \end{figure}$
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 (in the absence of fold-over).
Increasing $\Delta f$ increases the energy in the sidebands at the expense of energy at the carrier frequency.
The Pd patch fm.pd, shown below, demonstrates FM modulation.