(a). Consider the discrete-time signal xM[n] = sin 2π Mn), and assume N = 12. For M = 4, 5, 7, and 10, plot м[n] on the interval 0 ≤ n ≤ 2N - 1. Use stem to create your plots, and be sure to appropriately label your axes. What is the fundamental period of each signal? In general, how can the fundamental period be determined from arbitrary integer values of M and N? Be sure to consider the case in which M > N. (b). Consider the signal xk [n] = sin(wkn), where wk 2πk/5. For x[n] given by k = 1, 2, 4, and 6, use stem to plot each signal on the interval 0 ≤ n ≤9. All of the signals should be plotted with separate axes in the same figure using subplot. How many unique signals have you plotted? If two signals are identical, explain how different values of wk can yield the same signal. (c). Now consider the following three signals 2n 11[n] = cos +2 cos N 2n (3/2), 12[n] = 2 cos 23[n] = cos (2) + cos + 3n ' + 3 sin (5/7). 2N Assume N 6 for each signal. Determine whether or not each signal is periodic. If a signal is periodic, plot the signal for two periods, starting at n = 0. If the signal is not periodic, plot the signal for 0 ≤ n ≤ 4N and explain why it is not periodic. Remember to use stem and to appropriately label your axes.