Sampling of sinusoidal signals: aliasing Consider the following continuous-time sinusoidal signal xₐ(t) = sin 2π F₀t, -∝ to ∝ Since xₐ(t) is described mathematically, its sampled version can be described by values every T seconds. The sampled signal is described by the formula
x(n)=xₐ(nT) = sin 2π( F₀/Fs)n, -∝ to ∝ where F, 1/T is the sampling frequency. (a) Plot the signal x(n), 0 ≤ n ≤ 99 for Fs = 5 kHz and F₀ = 0.5, 2, 3, and 4.5 kHz. Explain the similarities and differences among the various plots. (b) Suppose that Fo = 2 kHz and F₁ = 50 kHz.
1. Plot the signal x(n). What is the frequency, fo of the signal x(n)?
2. Plot the signal y(n) created by taking the even-numbered samples of x(n). Is this a sinusoidal signal? Why? If so, what is its frequency?
