ECE-350 Midterm: ECE 350 Boise State Exam2 sample Solutions s05

• School: Boise State University
• Department: Electrical and Computer Engineering
• Course: ECE-350
• Professor: All

Document Summary

Sample exam #2 - solutions: for the following signal x(t) = cos(2t) + 2sin(3t) - cos(5t) - 1. 2 (b) graph the magnitude of ak versus . (c) graph the phase (angle) of ak versus . 3 /2 (d) if x(t) is passed through a real filter h(t) with magnitude and phase shown below. Then bk=ak*|h(jw)|e angles) b0 = 1*h(j0)=1*2=2, b1 =2*|h(j /2)| e b-1 = 2*|h(-j /2)| e b3 = 1*ej /2*|h(j3 /2)| e b-3 = 1*e-j /2*|h(-j 3 /2)| e. H(-j 3 /2)) = (1*1)ej(- /2+- /2) = (1*1)ej(- ) (e) what is y(t) for these fourier series coefficients? x(t)=1 + 4cos(( /2)t) + 2cos((3 /2)t+ /2) (cid:198) y(t)=1*h(j0) + 4*|h(j /2)|cos(( /2)t+ h(j /2)) + H(0)= 2 0, h(j /2)=2 0, h(j3 /2)=1 /2 y(t)=1*2 + 4*2cos(( /2)t+0) + 2*1cos((3 /2)t+ /2+ /2) y(t)=2 + 8cos(( /2)t) + 2cos((3 /2)t+ ) (10 points) determine the (exponential) fourier series of x(t) as shown below. x(t)