Final answer:
The question discusses sampling a continuous-time sinusoidal signal at different frequencies and the resulting plots that demonstrate the phenomenon of aliasing. As the signal frequency approaches or exceeds half the sampling frequency, aliasing distorts the representation of the original signal.
Step-by-step explanation:
The question concerns the sampling of a sinusoidal signal and the phenomenon of aliasing, which occurs when a continuous-time signal such as Xa(t) = sin 2F₀t is sampled at a discrete rate. The sampled signal is denoted as x(n) = sin(2πF₀/F₁ n), where F₁ = 1/T represents the sampling frequency. To explore the effects of sampling at different frequencies, we look at plots of the sampled signal x(n) for various values of the original signal frequency F₀ when the sampling frequency F₁ is fixed at 5 kHz.
Sampling a sinusoidal signal with frequencies F₀ = 0.5, 2, 3, and 4.5 kHz with a sampling frequency of 5 kHz and plotting the sampled values from 0 to 99 will illustrate the effects of aliasing. When F₀ is much less than half of F₁, the samples will represent the original signal well. However, as F₀ approaches F₁ or is greater than half of F₁, aliasing occurs, leading to a sampled signal that does not accurately represent the original sinusoidal waveform due to an insufficient sampling rate (according to the Nyquist theorem). For F₀ = 4.5 kHz, the sampling rate is just above the Nyquist rate, and we would see an almost accurate representation of the signal.