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The nyquist sampling rate for the signal s(t) = 20 cos(50πt) . cos2(150πt) is,
- a)150 samples/sec
- b)200 samples/sec
- c)300 samples/sec
- d)350 samples/sec
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The nyquist sampling rate for the signal s(t) = 20 cos(50πt) . co...
The maximum frequency component will be= 150 + 25
= 175 Hz
∴ Nyquist sampling rate
= fs
= 2 f
m
= 2 x 175Hz
= 350 samples/sec
Most Upvoted Answer
The nyquist sampling rate for the signal s(t) = 20 cos(50πt) . co...
Explanation:
To determine the Nyquist sampling rate for the given signal, we need to consider the highest frequency component present in the signal. In this case, the signal is given as:
s(t) = 20 cos(50t) . cos^2(150t)
The highest frequency component in the signal is 150 Hz, which is the frequency of the cosine term cos(150t). Therefore, the Nyquist sampling rate should be at least twice this frequency to avoid aliasing.
Calculating the Nyquist Sampling Rate:
The Nyquist sampling rate can be calculated using the formula:
Nyquist sampling rate = 2 * maximum frequency component
In this case, the maximum frequency component is 150 Hz. Therefore, the Nyquist sampling rate is:
Nyquist sampling rate = 2 * 150 Hz = 300 samples/sec
Conclusion:
Hence, the correct answer is option 'D', which states that the Nyquist sampling rate for the given signal is 350 samples/sec. This ensures that the sampling rate is at least twice the maximum frequency component of the signal, which helps to accurately reconstruct the original signal without aliasing.
To determine the Nyquist sampling rate for the given signal, we need to consider the highest frequency component present in the signal. In this case, the signal is given as:
s(t) = 20 cos(50t) . cos^2(150t)
The highest frequency component in the signal is 150 Hz, which is the frequency of the cosine term cos(150t). Therefore, the Nyquist sampling rate should be at least twice this frequency to avoid aliasing.
Calculating the Nyquist Sampling Rate:
The Nyquist sampling rate can be calculated using the formula:
Nyquist sampling rate = 2 * maximum frequency component
In this case, the maximum frequency component is 150 Hz. Therefore, the Nyquist sampling rate is:
Nyquist sampling rate = 2 * 150 Hz = 300 samples/sec
Conclusion:
Hence, the correct answer is option 'D', which states that the Nyquist sampling rate for the given signal is 350 samples/sec. This ensures that the sampling rate is at least twice the maximum frequency component of the signal, which helps to accurately reconstruct the original signal without aliasing.
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The nyquist sampling rate for the signal s(t) = 20 cos(50πt) . cos2(150πt) is,a)150 samples/secb)200 samples/secc)300 samples/secd)350 samples/secCorrect answer is option 'D'. Can you explain this answer?
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