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Two independent random voltage processes x1(t) and x2(t) are applied to an RC network as shown below. If the spectral power density of the two processes are respectively,
then, the output power spectral density will be
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two independent random voltage processes x1(t) and x2(t) are applied ...
Because the network is linear, the output voltage y(t) can be expressed as
y(t) = y1(t) + y2(t)
where, y1(t) : HP from input x1 (t) (assuming x2 (t) = 0)
and y2 (t) : HP from input x2 (t) (assuming x1 (t) = 0)
The transfer functions relating y(t) to x1 (t) and x2 (t) are H1and H2, respectively. These are given by
x1(t) and x2(t) are independent. So, the output y1(t) and y2(t) generated by them will also be independent.
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Community Answer
Two independent random voltage processes x1(t) and x2(t) are applied ...
Because the network is linear, the output voltage y(t) can be expressed as
y(t) = y1(t) + y2(t)
where, y1(t) : HP from input x1 (t) (assuming x2 (t) = 0)
and y2 (t) : HP from input x2 (t) (assuming x1 (t) = 0)
The transfer functions relating y(t) to x1 (t) and x2 (t) are H1and H2, respectively. These are given by
x1(t) and x2(t) are independent. So, the output y1(t) and y2(t) generated by them will also be independent.
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