Nyquist sampling rate condition and aliasing
Consider the signal:
X(t) = sin(0.5)/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 = 2*pi. 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.