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What is the sampling theorem in communication systems?
What is the sampling theorem in communication systems?
- It states that a signal must be sampled at a rate equal to its highest frequency component
- It states that a signal can be sampled at any rate without affecting its accuracy
- It states that a signal must be sampled at a rate at least twice its highest frequency component (correct)
- It states that a signal must be sampled at a rate half of its highest frequency component
What happens if a signal is not sampled according to the sampling theorem in communication systems?
What happens if a signal is not sampled according to the sampling theorem in communication systems?
- The signal will become independent of its frequency components
- The sampling rate will not affect the reconstructed signal
- The signal will remain accurately reconstructed
- The signal will lose information and introduce distortion during reconstruction (correct)
Why is it important to abide by the sampling theorem in communication systems?
Why is it important to abide by the sampling theorem in communication systems?
- To ensure accurate reconstruction of the original signal (correct)
- To simplify the communication system's hardware
- To make the communication system independent of frequency components
- To reduce the overall sampling rate
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Study Notes
Sampling Theorem in Communication Systems
- The sampling theorem states that a continuous-time signal can be perfectly reconstructed from its samples if the sampling rate is greater than twice the highest frequency component of the signal.
- The minimum sampling rate required to avoid aliasing is known as the Nyquist rate, which is twice the bandwidth of the signal.
Consequences of Insufficient Sampling
- If a signal is not sampled according to the sampling theorem, it leads to aliasing, which causes distortion and loss of original information.
- Aliasing occurs when the sampling rate is less than the Nyquist rate, resulting in overlapping of frequency spectra.
Importance of the Sampling Theorem
- Abiding by the sampling theorem ensures that the original continuous-time signal can be perfectly reconstructed from its samples.
- Failure to follow the sampling theorem can result in loss of information, distortion, and inaccurate representation of the original signal.
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