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If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for x(3t) and x(t/3)?
- a)ω0/3 and 3ω0 respectively
- b)6ω0 and ωC/6 respectively
- c)3ω0 and ω0/3 respectively
- d)ω0/6 and 6 respectively
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for...
Considering x(t)↔X(ω), then if y(t) = x(at)
Then for y(t)=x(3t): 
As the Nyquist rate for x(t) is ω0, ω0,X(ω) = 0 for |ω| > ω0/2
Considering y(t), Y(ω) = 0 for |ω/3| > ω0/2 =>Y(ω) = 0 for| ω| > 3ω0/2
Therefore Nyquist rate for y(t) is 2×3ω0/2=3ω0
for y(t) = x(t/3): Y(ω) = 3X(3ω)
As the Nyquist rate for x(t) is ω0,X(ω) = 0 for |ω| > ω0/2
Considering y(t), Y(ω) = 0 for |3ω| > ω0/2 => Y(ω) = 0 for |ω| > ω0/6
Therefore Nyquist rate for y(t) is 2 x ω0/6 = ω0/3
Most Upvoted Answer
If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for...
Nyquist rate is the minimum sampling rate required to accurately represent a continuous-time signal without any aliasing. It is equal to twice the highest frequency component in the signal.
Given that the Nyquist rate for x(t) is ω0, we need to find the Nyquist rates for x(3t) and x(t/3).
Nyquist rate for x(3t):
- The time scale of the signal x(3t) is compressed by a factor of 3 compared to x(t).
- This means the frequency components in x(3t) will be expanded by a factor of 3.
- Therefore, the Nyquist rate for x(3t) will be 3 times the Nyquist rate for x(t).
- So, the Nyquist rate for x(3t) is 3ω0.
Nyquist rate for x(t/3):
- The time scale of the signal x(t/3) is expanded by a factor of 3 compared to x(t).
- This means the frequency components in x(t/3) will be compressed by a factor of 3.
- Therefore, the Nyquist rate for x(t/3) will be 1/3 times the Nyquist rate for x(t).
- So, the Nyquist rate for x(t/3) is ω0/3.
Hence, the Nyquist rate for x(3t) is 3ω0 and the Nyquist rate for x(t/3) is ω0/3.
Therefore, the correct answer is option 'C': 3ω0 and ω0/3 respectively.
Given that the Nyquist rate for x(t) is ω0, we need to find the Nyquist rates for x(3t) and x(t/3).
Nyquist rate for x(3t):
- The time scale of the signal x(3t) is compressed by a factor of 3 compared to x(t).
- This means the frequency components in x(3t) will be expanded by a factor of 3.
- Therefore, the Nyquist rate for x(3t) will be 3 times the Nyquist rate for x(t).
- So, the Nyquist rate for x(3t) is 3ω0.
Nyquist rate for x(t/3):
- The time scale of the signal x(t/3) is expanded by a factor of 3 compared to x(t).
- This means the frequency components in x(t/3) will be compressed by a factor of 3.
- Therefore, the Nyquist rate for x(t/3) will be 1/3 times the Nyquist rate for x(t).
- So, the Nyquist rate for x(t/3) is ω0/3.
Hence, the Nyquist rate for x(3t) is 3ω0 and the Nyquist rate for x(t/3) is ω0/3.
Therefore, the correct answer is option 'C': 3ω0 and ω0/3 respectively.
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If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for x(3t) and x(t/3)?a)ω0/3 and 3ω0 respectivelyb)6ω0 and ωC/6 respectivelyc)3ω0 and ω0/3 respectivelyd)ω0/6 and 6 respectivelyCorrect answer is option 'C'. Can you explain this answer?
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If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for x(3t) and x(t/3)?a)ω0/3 and 3ω0 respectivelyb)6ω0 and ωC/6 respectivelyc)3ω0 and ω0/3 respectivelyd)ω0/6 and 6 respectivelyCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for x(3t) and x(t/3)?a)ω0/3 and 3ω0 respectivelyb)6ω0 and ωC/6 respectivelyc)3ω0 and ω0/3 respectivelyd)ω0/6 and 6 respectivelyCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for x(3t) and x(t/3)?a)ω0/3 and 3ω0 respectivelyb)6ω0 and ωC/6 respectivelyc)3ω0 and ω0/3 respectivelyd)ω0/6 and 6 respectivelyCorrect answer is option 'C'. Can you explain this answer?.
If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for x(3t) and x(t/3)?a)ω0/3 and 3ω0 respectivelyb)6ω0 and ωC/6 respectivelyc)3ω0 and ω0/3 respectivelyd)ω0/6 and 6 respectivelyCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for x(3t) and x(t/3)?a)ω0/3 and 3ω0 respectivelyb)6ω0 and ωC/6 respectivelyc)3ω0 and ω0/3 respectivelyd)ω0/6 and 6 respectivelyCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the Nyquist rate for x(t) is ω0, what will be the Nyquist rate for x(3t) and x(t/3)?a)ω0/3 and 3ω0 respectivelyb)6ω0 and ωC/6 respectivelyc)3ω0 and ω0/3 respectivelyd)ω0/6 and 6 respectivelyCorrect answer is option 'C'. Can you explain this answer?.
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