Arizona State University

EEE 203

Exam is closed book, closed notes except for one 8.5x11 sheet. You can use calculator. Show all your work on the pages provided. No extra pages (use back if necessary). The exam is worth 110 points in total with 100 points considered 100% and with 10 points considered extra credit. 1. (Fourier Series) (a) (5 pts) Write down the equation to represent a periodic signal 𝑥[𝑛] with period N using Fourier series coefficient 𝑎𝑘 (definition equation), i.e., 𝑥[𝑛] =? (b) (5 pts) Write down the equation to represent 𝑐𝑜𝑠𝜃 using 𝑒 𝑗𝜃 and 𝑒 −𝑗𝜃 . (c) (10 pts) Compute the Fourier series coefficients 𝑎𝑘 of the periodic signal 𝑥[𝑛] = cos ( 2𝜋 3 𝑛 − 𝜋 4 ) with period 𝑁 = 3. 𝑥[𝑛] = ∑ 𝑎𝑘𝑒 𝑗𝑘𝜔0𝑛 𝑘= 𝑐𝑜𝑠𝜃 = 1 2 (𝑒 𝑗𝜃 + 𝑒 −𝑗𝜃) 𝜔0 = 2𝜋 3 𝑥[𝑛] = ∑ 𝑎𝑘𝑒 𝑗𝑘2𝜋 3 �