GATE EC 2017 Set 1 — Question 50
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Communications → Digital Modulation & Detection → Digital Modulation (ASK, PSK, FSK, QAM)
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Question
In binary frequency shift keying (FSK), the given signal waveforms are
, and
,
where is the bit-duration interval and is in seconds. Both and are zero outside the interval . With a matched filter (correlator) based receiver, the smallest positive value of (in milliseconds) required to have and uncorrelated is
, and
,
where is the bit-duration interval and is in seconds. Both and are zero outside the interval . With a matched filter (correlator) based receiver, the smallest positive value of (in milliseconds) required to have and uncorrelated is
Correct answer
(B) 0.5 ms
Solution
Two signals and are uncorrelated if their correlation is zero. For zero-mean signals, this is equivalent to orthogonality:Substituting the given waveforms:Using the identity :Neglecting the high-frequency term (or noting that for , both terms become zero):For the smallest positive value, :Thus, the smallest positive value of is 0.5 ms.
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