ELEC 310 Midterm: ELEC 310 UVic Elec 310 Midterm 1 Soln Feb 4 2005

• School: University of Victoria
• Department: Electrical Engineering
• Course: ELEC 310
• Professor: All

Document Summary

/40: this is a closed book examination, a single sided 8. 5x11 inch crib note sheet is allowed. Hand in this sheet with your midterm: non-programmable calculators are allowed. 1: a periodic signal is given by x(t) = hsin(cid:16)18t + + 9 cos (25t + 3. 6) + 4 sin(cid:16)29t + 2(cid:17) (a) what is the fourier series representation of x(t)? (6 pts) x(t) = hcos(cid:16)18t + (cid:19) + 9 cos (25t + 3. 6) + 4 cos(cid:16)29t + 2 cos(cid:18)36t cos(cid:18)36t . + 9 cos (25t + 3. 6) + 4 cos(cid:16)29t + 2 . Which gives the real fourier series, the complex fourier series is given by x(t) = 2 e j(25t+3. 6) + (b) draw the amplitude spectrum of x(t)? (3 pts) 4 (c) what is the fundamental frequency of x(t)? (1 pts) All frequency components are integer multiples of 1 with no higher common factors of 25,29, and 36 so the fundamental frequency is 1 radian per seconds or 1.