Texts: For all problems, final answers without detailed work do not count. Partial marks are allocated for intermediate steps/calculations.
Problem 3 (20 points):
Consider the square-wave signal shown in Figure below. For this problem, assume A = 1 volts and T = 2 msec.
a) (6 points) Perform the Fourier Series Expansion (FSE) for the signal s(t).
s(t)
b) (6 points) Plot the functions s(t) and s_e(n=5) for -T < t < T using Matlab on the same graph, where the t-axis is in milliseconds and the y-axis is in volts. Compare them in terms of power and resemblance. Comment on your result.
T/2
3T/2
time
c) (6 points) Sketch, by hand or using Matlab, the PSD function for s_e(n=5) versus the frequency in Hz. Label your axes properly and write down (i.e. annotate) the respective power values/components on the graph.
d) (2 points) Compute the dynamic power range (DPR) for the signal s_e(n=5) in dBs. The student must show ALL the derivation or mathematical steps leading to the answer.
For all graphs, the axes must be labeled properly. For the parts where Matlab is used for plotting, the printout of the respective Matlab code is also required and should be included in the submission.
Hint: Express all variables (An, Bn, Power, etc.) in terms of A and T and do not substitute numerical values except when required and in plots.