One page 8 1 2 00 11 00 of hand written notes

Info icon This preview shows pages 5–8. Sign up to view the full content.

View Full Document Right Arrow Icon
One page ( 8 1 2 00 11 00 ) of HAND-WRITTEN notes permitted. OK to write on both sides. JUSTIFY your reasoning clearly to receive partial credit. Explanations are also REQUIRED to receive FULL credit for any answer. You must write your answer in the space provided on the exam paper itself. Only these answers will be graded. Circle your answers, or write them in the boxes provided. If space is needed for scratch work, use the backs of previous pages. Problem Value Score 1 40 2 30 3 30 No/Wrong Rec 3
Image of page 5

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

View Full Document Right Arrow Icon
PROBLEM sp-09-Q.1.1: (a) The signal plotted below is the sum of two sinusoids; determine the amplitudes and phases, as well as the frequencies in rad/s. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -5 -4 -3 -2 -1 0 1 2 3 Time t (sec) 1 C 4 cos ..2 =8/t C 3 =8/ (b) Express this signal as a sinusoid in standard form, i.e., A cos .! 0 t C '/ . s a .t/ D 5e j =3 e j 30 t C 5e j =3 e j 30 t Pick off the values from the positive frequency component to get s a .t/ D 10 cos .30 t =3/ (c) Express this signal as a sinusoid in standard form, i.e., A cos .! 0 t C '/ . s b .t/ D < e n . 10 j 30/e j 631t o The complex amplitude in polar form is . 10 j 30/ D 31:62e j1:893 , so s b .t/ D 31:62 cos .631t 1:893/
Image of page 6
PROBLEM sp-09-Q.1.2: The following M ATLAB code defines a periodic signal as the sum of sinusoids: tt = -10:0.00001:10; %- in seconds xxt = -5*ones(size(tt)); kk=12; xxt = xxt + (30/kk)*cos( 1.2*pi*kk*(tt-1/6) ); kk=10; xxt = xxt + real( (-5-12/j)*exp(j*1.6*pi*kk*tt) ); In the following questions, the signal x.t/ corresponds to the M ATLAB vector xxt . (a) Determine the fundamental frequency of x.t/ . ! 0 D 1:6 rad/s The signal x.t/ is the sum of three sinusoids with frequencies: 0 , 12.1:2 / D 14:4 , and 10.1:6 / D 16:0 . Using the greatest common divisor (GCD), we obtain the fundamental frequency as ! 0 D 0:1 gcd .0;144;160/ D 1:6 rad/s (b) The signal x.t/ is periodic, so it has a Fourier Series x.t/ D 1 X k D 1 a k e j! 0 kt Determine the values of all the nonzero coefficients f a k g , and list them in the table below. Write the Fourier coefficients in polar form as a k D k e j' k , where k 0 and < ' k . x.t/ D 5 C 2:5 cos .9.1:6 /t 12.1:2/ =6/ C< e f 13e j1:966 e j10.1:6 /t g We have DC ( k D 0/ , and the ninth and tenth harmonics. The phase of the second term is 2:4 , but must be changed to 0:4 to be in the correct range. Index k th Fourier coefficient k a k in polar form 0 5e j 9 1:25e j 0:4 9 1:25e j 0:4 10 6:5e j1:966 10 6:5e j1:966
Image of page 7

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

View Full Document Right Arrow Icon
PROBLEM sp-09-Q.1.3: (a) Recall Lab #2 where one sinusoid is broadcast from a transmitter, but a vehicle receives two signals, one
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern