Question

8. The complex exponential Fourier series of a real even signal has non-zero coefficients for non-negative k given by

a_k 2 0 1 3 2 -1 3 0.5 4 1 5 -2

a. What are the values for negative k?

b. What is the energy in the fundamental frequency?

c. What is the energy in the third and fourth harmonics?

d. What is the Fourier series in terms of sines and cosine if  $\omega _{0} = 3$?

Answer 1

ak for negahve & B. a for real & even signal non-negatie vales of k are equal. So a_k ak. So a 2 b. fundamental kal ak= a_k=3 3 is wľ tot -2 -1 so Eneragy in the fundamental 0.5 -4 -5 laltkule 2x3² 18 is -2 C. in the third & foult 93 - 0.5 au=1 Enernya lagle+ past 1941 194² - (0.5² x 2 + - ܐܕ܂ 2.5 it wo=3 for given values of ak f(t) ao tra, Coswott a a₂ Cosewott 293 Cas3 wot + 2a4 Cos4wot t.29, Casswot- 2+ 66053t +(-26.56t) + cosat +265120-465707 fit) - 2 + 6 CS3-20056t+ Co S9+ + 2 C03127-4Csist