Suppose that X(w) is real but not even. Can we conclude whether X[n]must be or cannot be real ? Can we conclude whether X[n]must be or cannot be even ? Remark: There is one wrong answer that will...

Extracted text: Suppose that X(w) is real but not even. Can we conclude whether X[n]must be or cannot be real ? Can we conclude whether X[n]must be or cannot be even ? Remark: There is one wrong answer that will still give you +1 point. Hint 1: This is based on the logical use of several properties of Fourier transform. Hint 2: If a" = a, what do you conclude ? Hint 3: If a sequence y[n] is Hermitian symmetric, is it true or not that y[n] is real if and only if y[n] is even ? X[n]must be real, and we cannot conclude on its even symmetry. nX[n]cannot be real, and we cannot conclude on its even symmetry. Oxn]must be even, and we cannot conclude whether it is real or not. Oxn]cannot be even, and we cannot conclude whether it is real or not. OXIN]must be real and must be even. xn]must be real and cannot be even. Xn)cannot be real and must be even. x(n]cannot be real and cannot be even. None of the above.