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A sinusoid x(t) = A cos2πfot is sampled at 5 times the Nyquist rate for 2.5 sec. A total of 250 samples are acquired value of fs and fm are given by
- a)fs = 200 Hz, fm = 50 Hz
- b)fs = 100 Hz, fm = 25 Hz
- c)ts = 50 Hz, fm = 12.5 Hz
- d)fs = 100 Hz, fm = 10 Hz
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A sinusoid x(t) = A cos2πfot is sampled at 5 times the Nyquist ra...
Sampling frequency,
fs = 5 x (N quilt rate)
= 5 x f0= 10f0
No of samples = 
= T x fs
= T x fs⇒ 250 = 2,5 x fs
Most Upvoted Answer
A sinusoid x(t) = A cos2πfot is sampled at 5 times the Nyquist ra...
Sampling a Sinusoid at 5 Times the Nyquist Rate
Given a sinusoid x(t) = A cos2fot, we are to sample it at 5 times the Nyquist rate for 2.5 sec. A total of 250 samples are acquired. We are to determine the value of fs and fm.
Nyquist Rate
The Nyquist rate, also known as the Nyquist frequency or folding frequency, is the minimum sampling rate required to accurately represent a signal. The Nyquist rate is given by:
fs ≥ 2fm
where fs is the sampling rate and fm is the highest frequency component in the signal.
Solution
Given:
x(t) = A cos2fot
fs = 5 × 2fm
T = 2.5 sec
N = 250
Sampling Rate
The sampling rate is given by:
fs = N/T
Substituting the given values, we get:
fs = 250/2.5 = 100 Hz
Highest Frequency Component
The highest frequency component in the signal is given by:
fm = fo/2 = 1/4fN
where fN is the Nyquist frequency and fo is the frequency of the sinusoid.
Substituting the given values, we get:
fN = fs/2 = 50 Hz
fo = 2fo = 100fN = 5000 Hz
fm = 1/4fN = 12.5 Hz
Therefore, the correct answer is option D: fs = 100 Hz, fm = 10 Hz.
Given a sinusoid x(t) = A cos2fot, we are to sample it at 5 times the Nyquist rate for 2.5 sec. A total of 250 samples are acquired. We are to determine the value of fs and fm.
Nyquist Rate
The Nyquist rate, also known as the Nyquist frequency or folding frequency, is the minimum sampling rate required to accurately represent a signal. The Nyquist rate is given by:
fs ≥ 2fm
where fs is the sampling rate and fm is the highest frequency component in the signal.
Solution
Given:
x(t) = A cos2fot
fs = 5 × 2fm
T = 2.5 sec
N = 250
Sampling Rate
The sampling rate is given by:
fs = N/T
Substituting the given values, we get:
fs = 250/2.5 = 100 Hz
Highest Frequency Component
The highest frequency component in the signal is given by:
fm = fo/2 = 1/4fN
where fN is the Nyquist frequency and fo is the frequency of the sinusoid.
Substituting the given values, we get:
fN = fs/2 = 50 Hz
fo = 2fo = 100fN = 5000 Hz
fm = 1/4fN = 12.5 Hz
Therefore, the correct answer is option D: fs = 100 Hz, fm = 10 Hz.
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A sinusoid x(t) = A cos2πfot is sampled at 5 times the Nyquist rate for 2.5 sec. A total of 250 samples are acquired value of fs and fm are given bya)fs = 200 Hz, fm = 50 Hzb)fs = 100 Hz, fm = 25 Hzc)ts = 50 Hz, fm = 12.5 Hzd)fs = 100 Hz, fm = 10 HzCorrect answer is option 'D'. Can you explain this answer?
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A sinusoid x(t) = A cos2πfot is sampled at 5 times the Nyquist rate for 2.5 sec. A total of 250 samples are acquired value of fs and fm are given bya)fs = 200 Hz, fm = 50 Hzb)fs = 100 Hz, fm = 25 Hzc)ts = 50 Hz, fm = 12.5 Hzd)fs = 100 Hz, fm = 10 HzCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A sinusoid x(t) = A cos2πfot is sampled at 5 times the Nyquist rate for 2.5 sec. A total of 250 samples are acquired value of fs and fm are given bya)fs = 200 Hz, fm = 50 Hzb)fs = 100 Hz, fm = 25 Hzc)ts = 50 Hz, fm = 12.5 Hzd)fs = 100 Hz, fm = 10 HzCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A sinusoid x(t) = A cos2πfot is sampled at 5 times the Nyquist rate for 2.5 sec. A total of 250 samples are acquired value of fs and fm are given bya)fs = 200 Hz, fm = 50 Hzb)fs = 100 Hz, fm = 25 Hzc)ts = 50 Hz, fm = 12.5 Hzd)fs = 100 Hz, fm = 10 HzCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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