Frequency Modulation

The general equation for an FM sound synthesizer is given by

$\displaystyle x(t) = A(t)\left[\cos(2\pi f_ct + I(t)\cos(2\pi f_mt + \phi_m) + \phi_c\right],$

where

$\displaystyle A(t)$	$\displaystyle \triangleq$	the time varying amplitude
$\displaystyle f_c$	$\displaystyle \triangleq$	the carrier frequency
$\displaystyle I(t)$	$\displaystyle \triangleq$	the modulation index
$\displaystyle f_m$	$\displaystyle \triangleq$	the modulating frequency
$\displaystyle \phi_m, \phi_c$	$\displaystyle \triangleq$	arbitrary phase constants $\displaystyle .$

``Music 270a: Modulation'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).