Consider the signal
x(t) =sin(0.5t) / 0.5t
(a) Find the Fourier transform X(Ω) of x(t).
(b) Is x(t) band limited? If so, find its maximum frequency Ωmax.
(c) Suppose that Ts = 2π. How does Ωs relate to the Nyquist frequency 2Ωmax? Explain.
(d) What is the sampled signal x(nTs) equal to? Carefully plot it and explain if x(t) can be reconstructed.