Question

To digitally encode the highest frequency in a signal successfully, it has to be sampled at at least _____ its frequency?

1) 1/2
2) 1/4
3) 1/8
4) 1/16

Answer 1

To digitally encode the highest frequency in a signal, it must be sampled at at least twice its frequency, aligning with option 1) 1/2, as dictated by the Nyquist theorem.

Step-by-step explanation:

To digitally encode the highest frequency in a signal successfully, it has to be sampled at at least twice its frequency, according to the Nyquist theorem. This means that the signal must be sampled at a minimum of the frequency specified by option 1) 1/2. The SI unit for frequency is the hertz (Hz), which is defined as one cycle per second.

For example, a frequency of 3 Hz means there are 3 cycles per second. When a signal is sampled at this rate, which is at least twice the maximum frequency present in the signal, it ensures that the sampling captures all the information in the signal and allows for proper reconstruction of the original signal from the sampled data.