$$x[n_1, n_2] = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$
6.1 The IIR filter with a transfer function:
8.1 The 2D DFT of the image:
$$H(z) = \frac{1}{1 - 0.5z^{-1} - 0.2z^{-2}}$$ $$x[n_1, n_2] = \begin{bmatrix} 1 & 2 \
$$X[k_1, k_2] = \begin{bmatrix} 10 & -2 \ -2 & -2 \end{bmatrix}$$
$$H(z) = 1 + 2z^{-1} + 3z^{-2}$$
3.2 The FFT of the sequence $x[n] = 1, 2, 3, 4$ is: b_1 = 2
5.1 The FIR filter with a length of 3 and coefficients $b_0 = 1, b_1 = 2, b_2 = 3$ has a transfer function:
2.2 The impulse response of the system is $h[n] = \delta[n] + 2\delta[n-1] + 3\delta[n-2]$.
7.1 The output of the downsampler is:
(b) The maximum and minimum values that can be represented by 12-bit unsigned binary numbers are 4095 and 0, respectively.
4.1 The transfer function of the filter is:
$$y[n] = x[2n]$$