Q22) [10 marks] For each of the following 10-point DFTs, determine a formula for the 10-point IDFT.
(a)
$X_0[k] = \begin{cases} 1 & k = 0 \\ 0 & k = 1,2,...,9 \end{cases}$
(b) $X_1[k] = 1$ $k = 0,1,2,...,9$
(c)
$X_2[k] = \begin{cases} 1 & k = 3,7 \\ 0 & k = 0,1,2,4,5,6,8,9 \end{cases}$
(d)
$X_3[k] = \cos(2\pi k/5)$ $k = 0,1,2,...,9$