S&S Midterm Quiz 1112-2 (Q).pdf

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Page 1 of 2 EE2023 Signals & Systems Quiz Semester 2 AY2011/12 Date: 8 March 2012 Time Allowed: 1.5 hours Q1. Consider a periodic signal, ( ) x t , modeled by the following equation: ( ) ( ) ( ) 3 2 2 3 2 2 3 5 2 3 2 j t j t j t j t x t je j e j e je = + + + + (a) What is the fundamental frequency of ( ) x t ? (b) By comparing ( ) x t with the Fourier Series expansion equation, ( ) o k k jk t x t c e ω =−∞ = , derive the magnitude, k c , and phase, k c , of the Fourier Series coefficients when k = 0, 1, 2 and 3. (c) An alternative method for evaluating the Fourier Series coefficients, k c , of ( ) x t is ( ) 0 2 1 T k j kt T c x t e dt T π = What is the value of T ? (d) Suppose the Fourier Series coefficients for the signal ( ) ( ) 4sin 3 y t t = is determined using the equation ( ) 0 2 1 T k j kt T c y t e dt T π = , where T is the value determined in part (c). Can the resulting Fourier Series coefficients be used to correctly synthesize ( ) y t via Fourier Series expansion ?
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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