Consider a sequence x[n] and its discrete-time Fourier transform X(e j ). The following is known: x[n] is real, x[0] = 0, x[1] > 0,

Consider a sequence x[n] and its discrete-time Fourier transform X(e^jω). The following is known:

 x[n] is real,

x[0] = 0,

x[1] > 0,

 |X(e^jω)|² = 5/4 – cosω.

Determine two distinct sequences x₁[n] and x₂[n] consistent with the given information.