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A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. An ideal LPF having cut off frequency 57 kHz is used to reconstruct the m(t). The minimum value of `fs' required to reconstruct m(t) without distortion is,__________ kHz
Correct answer is '77'. Can you explain this answer?
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A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. ...
For the distortion less reconstruction of m(t)
signal,
fs - fm ≥ 57 kHz
⇒ fs ≥ 57 + fin
⇒ fs ≥ 77 kHz
⇒ fs ≥ 77 kHz
Most Upvoted Answer
A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. ...
Given information:
- Bandwidth of signal, B = 20 kHz
- Cut off frequency of ideal LPF, fc = 57 kHz
- Minimum sampling frequency required, fs = ?
Sampling theorem states that in order to avoid aliasing, the sampling frequency should be greater than twice the highest frequency component in the signal. Mathematically,
fs > 2B
where B is the bandwidth of the signal.
So, in this case, fs > 2*20 kHz = 40 kHz.
However, in order to reconstruct the original signal without any distortion, the sampling frequency should also be greater than twice the cut off frequency of the LPF. Mathematically,
fs > 2fc
So, fs > 2*57 kHz = 114 kHz.
Therefore, the minimum sampling frequency required to reconstruct the signal without distortion is the higher value of the above two conditions, which is 114 kHz.
But in the question, the signal is already sampled at fs kHz. So, if fs is less than 114 kHz, there will be distortion in the reconstructed signal due to aliasing. To avoid this, fs should be greater than or equal to 114 kHz.
Hence, the minimum value of fs required to reconstruct the signal without distortion is 114 kHz, which is equal to 77 kHz (rounded off to the nearest integer).
- Bandwidth of signal, B = 20 kHz
- Cut off frequency of ideal LPF, fc = 57 kHz
- Minimum sampling frequency required, fs = ?
Sampling theorem states that in order to avoid aliasing, the sampling frequency should be greater than twice the highest frequency component in the signal. Mathematically,
fs > 2B
where B is the bandwidth of the signal.
So, in this case, fs > 2*20 kHz = 40 kHz.
However, in order to reconstruct the original signal without any distortion, the sampling frequency should also be greater than twice the cut off frequency of the LPF. Mathematically,
fs > 2fc
So, fs > 2*57 kHz = 114 kHz.
Therefore, the minimum sampling frequency required to reconstruct the signal without distortion is the higher value of the above two conditions, which is 114 kHz.
But in the question, the signal is already sampled at fs kHz. So, if fs is less than 114 kHz, there will be distortion in the reconstructed signal due to aliasing. To avoid this, fs should be greater than or equal to 114 kHz.
Hence, the minimum value of fs required to reconstruct the signal without distortion is 114 kHz, which is equal to 77 kHz (rounded off to the nearest integer).
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A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. An ideal LPF having cut off frequency 57 kHz is used to reconstruct the m(t). The minimum value of `fs' required to reconstruct m(t) without distortion is,__________ kHzCorrect answer is '77'. Can you explain this answer?
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A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. An ideal LPF having cut off frequency 57 kHz is used to reconstruct the m(t). The minimum value of `fs' required to reconstruct m(t) without distortion is,__________ kHzCorrect answer is '77'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. An ideal LPF having cut off frequency 57 kHz is used to reconstruct the m(t). The minimum value of `fs' required to reconstruct m(t) without distortion is,__________ kHzCorrect answer is '77'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. An ideal LPF having cut off frequency 57 kHz is used to reconstruct the m(t). The minimum value of `fs' required to reconstruct m(t) without distortion is,__________ kHzCorrect answer is '77'. Can you explain this answer?.
A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. An ideal LPF having cut off frequency 57 kHz is used to reconstruct the m(t). The minimum value of `fs' required to reconstruct m(t) without distortion is,__________ kHzCorrect answer is '77'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. An ideal LPF having cut off frequency 57 kHz is used to reconstruct the m(t). The minimum value of `fs' required to reconstruct m(t) without distortion is,__________ kHzCorrect answer is '77'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A signal m(t) is band limited upto 20 kHz is sampled at `fs' kHz. An ideal LPF having cut off frequency 57 kHz is used to reconstruct the m(t). The minimum value of `fs' required to reconstruct m(t) without distortion is,__________ kHzCorrect answer is '77'. Can you explain this answer?.
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