1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Fourier representation of CT peridic signals

  1. Feb 24, 2007 #1
    I want to find the Fourier coefficients for the following signal:

    [tex] \cos(2 \pi t)^2 [/tex]

    Can I simply use the identity?:

    [tex] \frac{1}{2} + \frac{\cos(2 \pi t)}{2} [/tex]

    And then use the complex definition:

    [tex] \frac{1}{2} + \frac{1}{4} (\exp{j2 \pi t} + \exp{-j2 \pi t}) [/tex]


    From the synthesis equation I can get:
    [tex] a_0 = \frac{1}{2} [/tex], [tex] a_1 = \frac{3}{4} [/tex]

    Thanks
     
    Last edited: Feb 24, 2007
  2. jcsd
  3. Feb 25, 2007 #2

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    [tex] \cos(2 \pi t)^2 [/tex] is a strange (non-standard) notation.

    If you mean [tex] \cos^2(2 \pi t)[/tex] then your method is almost correct - it equals [tex] \frac{1}{2} + \frac{\cos(4 \pi t)}{2} [/tex]


    If you mean [tex] \cos(4 \pi^2 t^2)[/tex] then it is not.
     
    Last edited: Feb 25, 2007
  4. Feb 25, 2007 #3
    I meant the first, and thanks for the correction.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...