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A signal is band-limited to 0 to 12 kHz. The signal spectrum is corrupted by additive noise which is band-limited to 10 to 12 kHz. Theoretically, the minimum rate in kilohertz at which the noisy signal must be sampled
so that the UNCORRUPTED PART of the signal spectrum can be recovered, is ____ kHz.
so that the UNCORRUPTED PART of the signal spectrum can be recovered, is ____ kHz.
(Important - Enter only the numerical value in the answer)
Correct answer is '20'. Can you explain this answer?
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A signal is band-limited to 0 to 12 kHz. Thesignal spectrum is corrupt...
correct answer is (22).
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A signal is band-limited to 0 to 12 kHz. Thesignal spectrum is corrupt...
To understand why the minimum sampling rate required to recover the uncorrupted part of the signal spectrum is 20 kHz, let's break down the problem into several key points.
Band-limited Signal:
The original signal is band-limited from 0 to 12 kHz. This means that the signal contains all its information and frequency components within this frequency range.
Band-limited Noise:
The additive noise in the signal is also band-limited, but from 10 to 12 kHz. This means that the noise components only exist within this frequency range and do not affect the lower frequencies.
Nyquist-Shannon Sampling Theorem:
According to the Nyquist-Shannon sampling theorem, to perfectly reconstruct a band-limited signal, the sampling rate must be at least twice the maximum frequency present in the signal. This is known as the Nyquist rate.
Recovering the Uncorrupted Part:
In this scenario, we want to recover the uncorrupted part of the signal spectrum, which means we need to sample at a rate that captures all the frequencies between 0 and 10 kHz.
Minimum Sampling Rate:
To recover the uncorrupted part of the signal spectrum, we need to sample at a rate that captures all the frequencies up to 10 kHz. According to the Nyquist-Shannon theorem, the minimum sampling rate required is twice the maximum frequency, which in this case is 10 kHz.
Therefore, the minimum sampling rate required to recover the uncorrupted part of the signal spectrum is 2 * 10 kHz = 20 kHz.
Conclusion:
In summary, the minimum sampling rate of 20 kHz is required because it allows us to capture all the frequencies up to 10 kHz, which is the highest frequency of the uncorrupted part of the signal spectrum. Sampling at a lower rate would result in the loss of information and the inability to recover the original signal accurately.
Band-limited Signal:
The original signal is band-limited from 0 to 12 kHz. This means that the signal contains all its information and frequency components within this frequency range.
Band-limited Noise:
The additive noise in the signal is also band-limited, but from 10 to 12 kHz. This means that the noise components only exist within this frequency range and do not affect the lower frequencies.
Nyquist-Shannon Sampling Theorem:
According to the Nyquist-Shannon sampling theorem, to perfectly reconstruct a band-limited signal, the sampling rate must be at least twice the maximum frequency present in the signal. This is known as the Nyquist rate.
Recovering the Uncorrupted Part:
In this scenario, we want to recover the uncorrupted part of the signal spectrum, which means we need to sample at a rate that captures all the frequencies between 0 and 10 kHz.
Minimum Sampling Rate:
To recover the uncorrupted part of the signal spectrum, we need to sample at a rate that captures all the frequencies up to 10 kHz. According to the Nyquist-Shannon theorem, the minimum sampling rate required is twice the maximum frequency, which in this case is 10 kHz.
Therefore, the minimum sampling rate required to recover the uncorrupted part of the signal spectrum is 2 * 10 kHz = 20 kHz.
Conclusion:
In summary, the minimum sampling rate of 20 kHz is required because it allows us to capture all the frequencies up to 10 kHz, which is the highest frequency of the uncorrupted part of the signal spectrum. Sampling at a lower rate would result in the loss of information and the inability to recover the original signal accurately.
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A signal is band-limited to 0 to 12 kHz. Thesignal spectrum is corrupted by additivenoise which is band-limited to 10 to 12 kHz.Theoretically, the minimum rate in kilohertzat which the noisy signal must be sampledso that the UNCORRUPTED PART of thesignal spectrum can be recovered, is ____kHz.(Important - Enter only the numerical value in the answer)Correct answer is '20'. Can you explain this answer?
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