Sampled Signal and Frequencies

In order to understand the highest frequency contained in a sampled signal, let's first clarify what a sampled signal is. A sampled signal is obtained by taking discrete samples of a continuous-time signal at regular intervals. The process of converting a continuous-time signal into a discrete-time signal is known as sampling.

When a continuous-time signal is sampled, it is converted into a discrete-time signal by taking samples at a specific rate, known as the sampling rate or sampling frequency (Fs). The sampling rate is typically measured in samples per second (Hz). Each sample represents the amplitude of the continuous-time signal at a specific point in time.

Nyquist-Shannon Sampling Theorem

According to the Nyquist-Shannon sampling theorem, in order to accurately reconstruct a continuous-time signal from its samples, the sampling rate must be at least twice the highest frequency component present in the signal. This is known as the Nyquist rate.

Highest Frequency in Sampled Signal

Given that the sampling rate is Fs, the highest frequency that can be accurately represented in the sampled signal is Fs/2. This is because the Nyquist rate is equal to twice the highest frequency, and therefore, the highest frequency is equal to the Nyquist rate divided by 2.

Explanation of Option B

Option B states that the highest frequency contained in the sampled signal is Fs/2. This is the correct answer because it aligns with the Nyquist-Shannon sampling theorem.

By sampling a continuous-time signal at a rate of Fs, we are able to accurately represent frequencies up to Fs/2 in the sampled signal. Frequencies above Fs/2 will result in aliasing, which is the phenomenon where different frequencies are indistinguishable from each other in the sampled signal.

Therefore, option B is the correct answer as it correctly identifies the highest frequency that can be contained in a sampled signal as Fs/2.