Editing Frequency modulation (section)

===Sinusoidal baseband signal===
Mathematically, a baseband modulating signal may be approximated by a [[Sine wave|sinusoid]]al [[continuous wave]] signal with a frequency ''f<sub>m</sub>''. This method is also named as single-tone modulation. The integral of such a signal <math>x_m(t) = cos(2\pi f_m t)</math> is:

:<math>\int_0^t x_m(\tau)d\tau = \frac{\sin\left(2\pi f_m t\right)}{2\pi f_m}\,</math>

In this case, the expression for y(t) above simplifies to:

:<math>y(t) = A_c \cos\left(2\pi f_c t + \frac{f_\Delta}{f_m} \sin\left(2\pi f_m t\right)\right)\,</math>

where the amplitude <math>A_m\,</math> of the modulating [[sine wave|sinusoid]] is represented in the peak deviation <math>f_\Delta = K_f A_m</math> (see [[frequency deviation]]).

The [[harmonic]] distribution of a [[sine wave]] carrier modulated by such a [[sinusoidal]] signal can be represented with [[Bessel function]]s; this provides the basis for a mathematical understanding of frequency modulation in the frequency domain.