Which theorem states that a frequency must be sampled at least twice to be reproduced reliably?

Which theorem states that a frequency must be sampled at least twice to be reproduced reliably?

• A. Fourier Theorem
• B. Nyquist Theorem
• C. Shannon's Theorem
• D. Sampling Theorem

Answer: (B)

The Nyquist Theorem specifically addresses the conditions necessary for accurate signal sampling and reconstruction. It posits that to accurately capture and reproduce a continuous signal without aliasing, the signal must be sampled at a frequency that is at least twice the highest frequency present in the signal. This fundamental principle highlights the importance of sampling rate in digital signal processing, ensuring that all necessary information is retained without distortion or loss. In the context of computed tomography (CT) and other imaging modalities, understanding the Nyquist Theorem is crucial because it relates to how image data is sampled and reconstructed from raw data, ultimately affecting image quality. The theorem helps in preventing artifacts that can arise from insufficient sampling, allowing for clearer and more accurate images in medical imaging applications.

The Nyquist Theorem specifically addresses the conditions necessary for accurate signal sampling and reconstruction. It posits that to accurately capture and reproduce a continuous signal without aliasing, the signal must be sampled at a frequency that is at least twice the highest frequency present in the signal. This fundamental principle highlights the importance of sampling rate in digital signal processing, ensuring that all necessary information is retained without distortion or loss.

In the context of computed tomography (CT) and other imaging modalities, understanding the Nyquist Theorem is crucial because it relates to how image data is sampled and reconstructed from raw data, ultimately affecting image quality. The theorem helps in preventing artifacts that can arise from insufficient sampling, allowing for clearer and more accurate images in medical imaging applications.