Given the DFT coefficients represented by the vector [mathbf{X}=left[begin{array}{llllllll}9 & 1 & 1 & 9 & 1 & 1 & 1 & 1end{array} ight]^{mathrm{T}}] (a)

Given the DFT coefficients represented by the vector

\[\mathbf{X}=\left[\begin{array}{llllllll}9 & 1 & 1 & 9 & 1 & 1 & 1 & 1\end{array}\right]^{\mathrm{T}}\]

(a) determine its length-8 IDFT;

(b) determine the sequence whose length- 8 DFT is given by \(Y(k)=W_{8}^{-4 k} X(k)\).