User:CSeguinot

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Such a modulated signal m(t) and it's complex representation ${\tilde {m}}(t)$ is :

$m(t)=a(t)\cos(2\pi F_{0}t+\phi (t))$

${\tilde {m}}(t)=a(t)e^{(j(2\pi F_{0}t+\phi (t)))}=a(t)e^{j\phi (t)}e^{j2\pi F_{0}t}$

The complex representation is obtained by replacing the cos function by an exponent function. The real signal correspond to the real part of the complex signal $m(t)={\text{Re}}({\tilde {m}}(t))$.