What occurs when a 60 cycle sine wave is sampled at 100 hertz?

What occurs when a 60 cycle sine wave is sampled at 100 hertz?

• A. Aliasing
• B. Digital filtering
• C. Overlap of data
• D. Subharmonic response

Answer: (A)

Sampling a 60 cycle sine wave at 100 hertz leads to aliasing, which occurs when the sampling rate is insufficient to capture the frequency of the signal accurately. According to the Nyquist theorem, to accurately reconstruct a signal, it needs to be sampled at least twice its highest frequency. In this case, the sine wave has a frequency of 60 Hz, meaning it should be sampled at a minimum of 120 Hz to avoid aliasing. When the wave is instead sampled at only 100 Hz, the sampling frequency is less than double that of the sine wave, which results in the distortion of the signal's representation. The sampled points may not accurately reflect the true amplitude of the sine wave at various points in time, causing a misinterpretation of its frequency. This is known as aliasing, where higher frequency components of a signal appear as lower frequency components when sampled improperly. Understanding the implications of sampling frequency is crucial for accurately capturing and interpreting signals in electroencephalography and other fields of signal processing.

Sampling a 60 cycle sine wave at 100 hertz leads to aliasing, which occurs when the sampling rate is insufficient to capture the frequency of the signal accurately. According to the Nyquist theorem, to accurately reconstruct a signal, it needs to be sampled at least twice its highest frequency. In this case, the sine wave has a frequency of 60 Hz, meaning it should be sampled at a minimum of 120 Hz to avoid aliasing.

When the wave is instead sampled at only 100 Hz, the sampling frequency is less than double that of the sine wave, which results in the distortion of the signal's representation. The sampled points may not accurately reflect the true amplitude of the sine wave at various points in time, causing a misinterpretation of its frequency. This is known as aliasing, where higher frequency components of a signal appear as lower frequency components when sampled improperly.

Understanding the implications of sampling frequency is crucial for accurately capturing and interpreting signals in electroencephalography and other fields of signal processing.