# Suppressed  Carrier Wave
Derive expressions from which it will be evident whether the
communication channel has more power as an AM signal with
a suppressed carrier wave or as an AM signal with the carrier
wave present. Assume the voltage signal, $v(t)$ and $m(t)$, as in
the previous figure. Modulating (LF) sinusoidal signal has
amplitude $A$ and frequency $f_{LF}$ Hz, cosine wave RF carrier has
amplitude $1$ and frequency $f_{VF}$.


According to $P_t = P_c + P_{USB} + P_{LSB} $ the total transmitting power has to be split among carrier, upper and lower side band.
With the carrier wave suppressed, the modulating signal will take up all of the available transmission power instead.

For a standard AM signal with the above requirements, the formula is:
$$ s(t) = (1+A \cos(2\pi f_{LF}t)) \cdot \cos(2\pi f_{VF} t)$$

With the power of a wave signal given by $P=\frac{(v_m/\sqrt{2})^2}{2}$ (where $v_m$ is max of cosine signal),
our sideband power is $2* \frac{(A/\sqrt{2})^2}{2} = \frac{A^2}{2}$ 
and our carrier power $\frac{1}{2}$, equal to the power gained in DSB-SC.