x[n] is a real-valued finite-length sequence of length 10 and is nonzero in the interval from 0 to 9, i.e., 

x[n] = 0,           n < 0, n ≥ 10,

x[n] ≠ 0,           0 ≤ n ≤ 9.

X(e^jω) denotes the Fourier transform of x[n], and X[k] denotes the 10-point DFT of x[n]. Determine a choice for x[n] so that X[k] is real valued for all k and 

X(e^jω) = A(ω)e^jaω,        |ω| < π,

Where A(ω) is real and α is a nonzero real constant.