Digital Signal Processing Sanjit K Mitra 3rd Edition Solution Manual -
4.1 The transfer function of the filter is:
$$X[k] = \begin{bmatrix} 10 & -2+j2 & -2 & -2-j2 \end{bmatrix}$$
3.2 The FFT of the sequence $x[n] = 1, 2, 3, 4$ is:
2.1 (a) The even part of the signal $x[n] = \cos(0.5\pi n)$ is $x_e[n] = \cos(0.5\pi n)$.
8.1 The 2D DFT of the image:
(b) The odd part of the signal $x[n] = \cos(0.5\pi n)$ is $x_o[n] = 0$.
$$X[k_1, k_2] = \begin{bmatrix} 10 & -2 \ -2 & -2 \end{bmatrix}$$