ECE-350 Midterm: ECE 350 Boise State Exam2 sample Solutions s10

• 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. = 1 + 4cos(( /2)t) + 2cos((3 /2)t+ /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. 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) 0 k odd k even: a) tables: xa(j ) = 2sin( t1)/ = 2sin( )/ (from table 4. 2, eq#8) 1 j t dt etx: xb(t) = xa(t)+xa(t-2) (time shift & linearity) j. )1( j dt e e t j t j. Or- xb(t) = xa((t-1)/2) (cid:198) xb(j ) = 2x(2j )e-j = 2e-j sin(2 )/ .