ex3_solns

# ex3_solns - Name Exam 3 363M CM 1(25 points Finding the...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Name Exam 3 363M CM 1. (25 points) Finding the energy in a given bandwidth For the signal x(t) with spectrum shown below: . _ . _ _ _ _ _ _ -_. . _ . _ _ _ _ . _ . _ . _ _ . -g O -100 £0 -60 40 -20 0 20 4O 60 80 100 Frequency (radians/sec) Determine the percentage of the total energy in x(t) between 20 and 60 radians/ sec. R AID .no '20 L”) Sro CT : ’E—ES 313)“) g ‘iz‘m 1% (9250* g Lizacvd #2 110?“) It! ~90 no ‘20 lo ‘0 7.qu 0 + 401: :‘LK‘Lquc-f-(Qp 10+ 2(9qu «HQ: 1 ‘i .m. 2H L” 0 9:0 “\ 4,3431: f0 r“ «{on CINE“ 2 .40 101'- 4T? : , X Li wing 2 u " —— Lawué 1" -810 q: i 7f? Name CM 2. (30 points) System analysis with the Fourier Transform Consider a linear time invariant system with impulse response given by h(t) = -3—sinc 22: 27: with input x(t) = 3 sinc2 cos(t — 3) Jr 71' The output of the system is y(t) . Show all of your work and draw a BOX around your ﬁnal answer. a) Determine X (m) . b) Sketch the spectrum of X ((0) (magnitude and phase) accurately labeling the axes and important points. c) Determine H (w) . d) Sketch the spectrum of H ((0) (magnitude and phase) accurately labeling the axes and important points. w 2'3“) 6) Determine y(t), the output of the system. Z I‘ 3 2’ (lo Ca) For 11(9) 3 €m8<\$n> Yul”) :TrJu “) D XXI») E’V‘IT K: ,3 Kim) = 2 )4 I ‘\ W Name CM 3. (25 points) Fourier Series of a Periodic Signal The following set of questions refer to the signal below (a) What is the fundamental frequency of x(t) in (rad/s)? (b) Find an expression for the Fourier Series Coefﬁ answer as much as possible. cients, ck, of x(t). Simplify your @ 7; .5ng w” 7 7:2 ’ r 2 Z t KW A“ (My a ‘3’“; fwd 0/é*f‘2a4 at] K 1 -2 0 ’0 W0 Kaleb o ﬂ’t’woe‘ a") eqkwo “I ‘F e w ,I 6-0 / + e a t : i “mi—“wax - 2 #1 2 L7 Milo 1 170*“? 0 )ﬁwo " -‘ a“ +9? - u a .1 20045103 M2] 2 ~~Mg§gu~y ﬂ~m w A ’ l W 4Kujo ~y<.—A W»~~ Haw/W"Hﬂ-“ ~ ~ ‘4.“ ¢¥ e l ws (CW>~/; ‘ lk1 2 {A )K., A 9": ‘Jm ” # A Name CM 4. (20 points) Properties of the Fourier Transform Show that if a signal, x(t), is real and even, then the Fourier Transform of the signal, X(co), is also real and even. (7/ a m i ’33 K m new 4th z / 90/5 - «(1-3 QM (wt X/w) = :5398 “’1”; .Lq’tw W d M 'T M avgv‘ don; : UJJ : {GK/k3 om/wt3Jé Cniiautmg, Over 1‘ T '30 .. :: 40?) 00qu J/yw) g {53/63 VJ (a 35/43 Jo dA/p’ah/PVVW ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern