(Solved): 4.4 Assume that the DFT of an \( N \)-point sequence \( x(n) \) is given by \ ...

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4.4 Assume that the DFT of an \( N \)-point sequence \( x(n) \) is given by \[ X(k)=\left\{\begin{array}{ll} \frac{N}{2} \mathrm{e}^{\mathrm{i} \beta}, & k=k_{0} \\ \frac{N}{2} \mathrm{e}^{-\mathrm{j} \beta}, & k=N-k_{0} \\ 0, & \text { otherwise } \end{array}\right. \] where \( 0