Editing Double-sideband suppressed-carrier transmission (section)

===Distortion and attenuation===
For demodulation, the demodulation oscillator's frequency and phase must be exactly the same as the modulation oscillator's, otherwise, distortion and/or attenuation will occur.

To see this effect, take the following conditions:
*Message signal to be transmitted: <math>f(t)</math>
*Modulation (carrier) signal: <math>V_c\cos(\omega_c t)</math>
*Demodulation signal (with small frequency and phase deviations from the modulation signal): <math>V'_c\cos\left[(\omega_c+\Delta\omega)t + \theta\right]</math>

The resultant signal can then be given by
:<math>f(t) \times V_c\cos(\omega_c t) \times V'_c\cos\left[(\omega_c+\Delta\omega)t + \theta\right]</math>
::<math>=\frac{1}{2}V_c V'_c f(t) \cos\left(\Delta\omega\cdot t+\theta\right) + \frac{1}{2}V_c V'_c f(t) \cos\left[(2\omega_c+\Delta\omega)t+\theta\right]</math>
::<math>\xrightarrow{\text{After low pass filter}} \frac{1}{2}V_c V'_c f(t) \cos\left(\Delta\omega\cdot t+\theta\right)</math>

The <math>\cos\left(\Delta\omega\cdot t+\theta\right)</math> terms results in distortion and attenuation of the original message signal. In particular, if the frequencies are correct, but the phase is wrong, contribution from <math>\theta</math> is a constant attenuation factor, also <math>\Delta\omega\cdot t</math> represents a cyclic inversion of the recovered signal, which is a serious form of distortion.

[[File:Demodulation distortion diagram.png]]