Sampling of sinusoidal signals: aliasing Consider the following continuous-time sinusoid...

Sampling of sinusoidal signals: aliasing Consider the following continuous-time sinusoidal signal

Since x_a (t) is described mathematically, its sampled version can be described by values every T seconds. The sampled signal is described by the formula

where F_s = 1/T is the sampling frequency.

(a) Plot the signal x(n), for F_s = 5 kHz and F₀ = 0.5, 2, 3, and 4.5 kHz. Explain the similarities and differences among the various plots.

(b) Suppose that F₀ = 2 kHz and F_s = 50 kHz.

1. Plot the signal x (n) . What is the frequency f_o 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?