File:FM Modulated Signal.svg

A graph showing an FM modulated signal. The modulating (message) and carrier signals are given respectively as:

• ${\displaystyle x_{m}(t)=0.65\left[0.2\sin(t)+0.5\cos(2t)+\cos(4.5t)\right]}$
• ${\displaystyle x_{c}(t)=A\cos(2\pi f_{c})\,}$

where

• ${\displaystyle A=2\,}$
• ${\displaystyle f_{c}=3\,}$

The modulated signal is then given by:

${\displaystyle y(t)A\cos \left(2\pi \int _{0}^{t}\left[f_{c}+x_{m}(\tau )f_{\Delta }\right]\,d\tau \right)}$

where the frequency deviation is given by:

• ${\displaystyle f_{\Delta }=0.15\,}$