What happens if the sampling rate is too low according to the Nyquist Theorem?

What happens if the sampling rate is too low according to the Nyquist Theorem?

• A. The resulting images will be clearer
• B. The original signal cannot be accurately reconstructed
• C. It leads to faster imaging times
• D. It increases resolution significantly

Answer: (B)

The Nyquist Theorem states that to accurately reconstruct a signal, the sampling rate must be at least twice the highest frequency present in the signal. If the sampling rate is too low, aliasing occurs, meaning that high-frequency components are misrepresented as lower frequencies. This results in distortions that prevent the accurate reconstruction of the original signal. Consequently, the loss of fidelity in the reconstructed image can lead to significant errors and artifacts, compromising the overall quality of the image produced. Therefore, ensuring that the sampling rate meets or exceeds the requirements set by the Nyquist Theorem is crucial for achieving accurate representations in imaging.

The Nyquist Theorem states that to accurately reconstruct a signal, the sampling rate must be at least twice the highest frequency present in the signal. If the sampling rate is too low, aliasing occurs, meaning that high-frequency components are misrepresented as lower frequencies. This results in distortions that prevent the accurate reconstruction of the original signal. Consequently, the loss of fidelity in the reconstructed image can lead to significant errors and artifacts, compromising the overall quality of the image produced. Therefore, ensuring that the sampling rate meets or exceeds the requirements set by the Nyquist Theorem is crucial for achieving accurate representations in imaging.