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How to sample the signal in case of intensity modulation?

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dotronghop

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I want to sample a signal in optical communication (like infrared communication)
The channel input X(t) is the instantaneous optical power (not the amplitude).
The average transmitted power Pt is given by
519201121208am.png

Where T is the bit period. The pulse will be the rectangular pulse.
Suppose that X(t) is constant, then X(t)=Pt

My question is how to sample this signal. For example with Pt=20mW, T=10ns, and I sample this signal with the interval of time deltaT=1ns. Then, the signal will be an array of 11 samples:
X(0)=20; X(1)=20; X(2)=20; ... ; X(10)=20;

But if the interval of time deltaT=0.1ns, the sample signal will be an array of 110 samples:
X(0)=20; X(1)=10; ...; X(110)=20;

I guess that I missed something here. But the average power is 20, so the instantaneous power will be 20 at any point of time. Am I right?
 

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