(b) The maximum and minimum values that can be represented by 12-bit unsigned binary numbers are 4095 and 0, respectively.
2.1 (a) The even part of the signal $x[n] = \cos(0.5\pi n)$ is $x_e[n] = \cos(0.5\pi n)$.
$$X[k] = \begin{bmatrix} 10 & -2+j2 & -2 & -2-j2 \end{bmatrix}$$
This solution manual provides a comprehensive set of solutions to the problems and exercises in the 3rd edition of Sanjit K. Mitra's "Digital Signal Processing". The solutions are intended to help students understand the concepts and principles of digital signal processing. (b) The maximum and minimum values that can
$$X[k_1, k_2] = \begin{bmatrix} 10 & -2 \ -2 & -2 \end{bmatrix}$$
$$H(z) = \frac{1}{1 - 0.5z^{-1} - 0.2z^{-2}}$$
is:
$$X[k] = \begin{bmatrix} 10 & -2+j2 & -2 & -2-j2 \end{bmatrix}$$
$$x[n_1, n_2] = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$
4.1 The transfer function of the filter is: Mitra's "Digital Signal Processing"
$$h[n] = 0.5^n u[n]$$
3.2 The FFT of the sequence $x[n] = 1, 2, 3, 4$ is:
6.1 The IIR filter with a transfer function: (b) The maximum and minimum values that can
$$y[n] = x[2n]$$
2.2 The impulse response of the system is $h[n] = \delta[n] + 2\delta[n-1] + 3\delta[n-2]$.