Question 1. Find the DTFT $X(\omega)$ for the following signals.
(a) $x_1[n] = \{1, -2, 0.5, -1, 3, 1\}$
(b) $x_2[n] = u[n] - u[n - 20]$
(c) $x_3[n] = x_2[n - 10]$
(d) $x_4[n] = x_2[n] \exp(j0.5\pi n)$
Plot the four magnitude spectra $|X(\omega)|$ on Matlab. Clearly label your plots.
Use these plots to measure the frequency at which the energy density is maximum.