(New page: Synchronous Demodulation -> Assume that wc > wm and consider the signal: y(t)=x(t)coswct The original signal can be recovered by modulating y(t) with the same sinusoidal ca...) |
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Synchronous Demodulation -> | Synchronous Demodulation -> | ||
| − | Assume that | + | Assume that <math>w_c > w_m </math> and consider the signal: |
| − | y(t)=x(t) | + | y(t)=x(t)<math>cosw_c t</math> |
The original signal can be recovered by modulating y(t) with the same sinusoidal carrier and applying a low pass filter to the | The original signal can be recovered by modulating y(t) with the same sinusoidal carrier and applying a low pass filter to the | ||
result. | result. | ||
| − | w(t)=y(t) | + | w(t)=y(t)<math>cosw_c</math>t |
| − | =x(t)cos^2 | + | =x(t)<math>cos^2 w_c</math>t |
| + | Use the trig identity | ||
| + | <math>cos^2 w_c</math>t=(1/2)+(1/2)<math>2cosw_c</math>t | ||
| + | We can rewrite as | ||
| + | w(t)=(1/2)x(t)=(1/2)x(t)<math>2cosw_c</math>t | ||
| + | In this process the demodulating signal is assumed to be synchronized in phase with the modulating signal. | ||
Latest revision as of 17:18, 29 July 2009
Synchronous Demodulation ->
Assume that $ w_c > w_m $ and consider the signal: y(t)=x(t)$ cosw_c t $ The original signal can be recovered by modulating y(t) with the same sinusoidal carrier and applying a low pass filter to the result. w(t)=y(t)$ cosw_c $t =x(t)$ cos^2 w_c $t Use the trig identity $ cos^2 w_c $t=(1/2)+(1/2)$ 2cosw_c $t We can rewrite as w(t)=(1/2)x(t)=(1/2)x(t)$ 2cosw_c $t In this process the demodulating signal is assumed to be synchronized in phase with the modulating signal.
