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A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is
- a)5
- b)12
- c)15
- d)20
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A band-limited signal with a maximum frequency of 5 kHz is to be sampl...
Explanation: fs (min) =2fm
fs (min) =2*5 =10 KHz
So, fs >=1o KHz.
Most Upvoted Answer
A band-limited signal with a maximum frequency of 5 kHz is to be sampl...
**Sampling Theorem**
The sampling theorem states that in order to accurately reconstruct a band-limited signal from its samples, the sampling frequency must be at least twice the maximum frequency present in the signal. This is known as the Nyquist rate.
**Given Information**
In this question, we are given that the maximum frequency of the band-limited signal is 5 kHz.
**Calculating Nyquist Rate**
To find the minimum sampling frequency required, we need to calculate the Nyquist rate using the formula:
Nyquist rate = 2 * maximum frequency
Substituting the given maximum frequency of 5 kHz into the formula, we get:
Nyquist rate = 2 * 5 kHz = 10 kHz
Therefore, the minimum sampling frequency required to accurately sample the band-limited signal is 10 kHz.
**Analyzing the Options**
Now, let's analyze the given options:
a) 5 kHz: This is the option stated as "not valid." The Nyquist rate calculated above is 10 kHz, which is greater than 5 kHz. Therefore, this option is not valid.
b) 12 kHz: The Nyquist rate calculated above is 10 kHz, which is less than 12 kHz. Therefore, this option is valid.
c) 15 kHz: The Nyquist rate calculated above is 10 kHz, which is less than 15 kHz. Therefore, this option is valid.
d) 20 kHz: The Nyquist rate calculated above is 10 kHz, which is less than 20 kHz. Therefore, this option is valid.
**Conclusion**
Based on the calculations and analysis, we can conclude that the sampling frequency of 5 kHz is not valid according to the sampling theorem. The correct answer is option 'A'.
The sampling theorem states that in order to accurately reconstruct a band-limited signal from its samples, the sampling frequency must be at least twice the maximum frequency present in the signal. This is known as the Nyquist rate.
**Given Information**
In this question, we are given that the maximum frequency of the band-limited signal is 5 kHz.
**Calculating Nyquist Rate**
To find the minimum sampling frequency required, we need to calculate the Nyquist rate using the formula:
Nyquist rate = 2 * maximum frequency
Substituting the given maximum frequency of 5 kHz into the formula, we get:
Nyquist rate = 2 * 5 kHz = 10 kHz
Therefore, the minimum sampling frequency required to accurately sample the band-limited signal is 10 kHz.
**Analyzing the Options**
Now, let's analyze the given options:
a) 5 kHz: This is the option stated as "not valid." The Nyquist rate calculated above is 10 kHz, which is greater than 5 kHz. Therefore, this option is not valid.
b) 12 kHz: The Nyquist rate calculated above is 10 kHz, which is less than 12 kHz. Therefore, this option is valid.
c) 15 kHz: The Nyquist rate calculated above is 10 kHz, which is less than 15 kHz. Therefore, this option is valid.
d) 20 kHz: The Nyquist rate calculated above is 10 kHz, which is less than 20 kHz. Therefore, this option is valid.
**Conclusion**
Based on the calculations and analysis, we can conclude that the sampling frequency of 5 kHz is not valid according to the sampling theorem. The correct answer is option 'A'.
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A band-limited signal with a maximum frequency of 5 kHz is to be sampl...
**Sampling Theorem**
The sampling theorem states that in order to accurately reconstruct a band-limited signal, the sampling frequency must be at least twice the maximum frequency present in the signal. Mathematically, this can be expressed as:
Fs ≥ 2 * Fmax
where Fs is the sampling frequency and Fmax is the maximum frequency of the signal.
**Analysis**
In this question, we are given that the band-limited signal has a maximum frequency of 5 kHz. We need to determine which sampling frequency is not valid according to the sampling theorem.
Let's analyze each option:
a) 5 kHz: In this case, the sampling frequency is equal to the maximum frequency of the signal. According to the sampling theorem, the sampling frequency must be greater than the maximum frequency, so this option is not valid.
b) 12 kHz: The sampling frequency of 12 kHz is greater than twice the maximum frequency of 5 kHz (2 * 5 kHz = 10 kHz). Therefore, this option is valid.
c) 15 kHz: The sampling frequency of 15 kHz is also greater than twice the maximum frequency of 5 kHz. Therefore, this option is valid.
d) 20 kHz: The sampling frequency of 20 kHz is greater than twice the maximum frequency of 5 kHz. Therefore, this option is valid.
**Conclusion**
Based on the analysis, we can conclude that the sampling frequency of 5 kHz is not valid according to the sampling theorem. The correct answer is option A.
The sampling theorem states that in order to accurately reconstruct a band-limited signal, the sampling frequency must be at least twice the maximum frequency present in the signal. Mathematically, this can be expressed as:
Fs ≥ 2 * Fmax
where Fs is the sampling frequency and Fmax is the maximum frequency of the signal.
**Analysis**
In this question, we are given that the band-limited signal has a maximum frequency of 5 kHz. We need to determine which sampling frequency is not valid according to the sampling theorem.
Let's analyze each option:
a) 5 kHz: In this case, the sampling frequency is equal to the maximum frequency of the signal. According to the sampling theorem, the sampling frequency must be greater than the maximum frequency, so this option is not valid.
b) 12 kHz: The sampling frequency of 12 kHz is greater than twice the maximum frequency of 5 kHz (2 * 5 kHz = 10 kHz). Therefore, this option is valid.
c) 15 kHz: The sampling frequency of 15 kHz is also greater than twice the maximum frequency of 5 kHz. Therefore, this option is valid.
d) 20 kHz: The sampling frequency of 20 kHz is greater than twice the maximum frequency of 5 kHz. Therefore, this option is valid.
**Conclusion**
Based on the analysis, we can conclude that the sampling frequency of 5 kHz is not valid according to the sampling theorem. The correct answer is option A.
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A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid isa)5b)12c)15d)20Correct answer is option 'A'. Can you explain this answer?
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