The signal x(t) has a Fourier transform X() = u( + 1) u( 1) thus

The signal x(t) has a Fourier transform X(Ω) = u(Ω + 1) − u(Ω − 1) thus it is band-limited, suppose we generate a new signal y(t) = (x* x)(t), i.e., it is the convolution of x(t) with itself.

(a) Find x(t) and indicate its support.

(b) Is it true that y(t) = x(t)? to determine if this is so calculate Y(Ω).

(c) What would be the largest value of the sampling period T_s that would not cause aliasing when sampling y(t)?

(d) What happens if we choose T_s = π? how does this relate to the Nyquist condition?