1. Not finding help here? Sign up for a free 30min 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!

Help With Fourier Series Expansion of a Periodic Function

  1. Dec 3, 2011 #1
    1. The problem statement, all variables and given/known data

    f(t) defined by f(t) = |t| for (-pi,pi) and f(t+2pi)=f(t)

    the graph is just ^^^

    where w=2pi/T = 1

    2. Relevant equations

    Periodic function using Trigonometric from

    Even Function f(t) = (1/2)anot + (the sum from n=1 to inf) (an)*COS(nwt), where an = 4/T Integrated from 0 to T/2 f(t)*COS(nwt)dt, where T= 2pi

    3. The attempt at a solution

    My answer: I used integration by parts and calculated pi/2 +(the sum from n=1 to inf) (4/(pi)n^2)*COS(nt),

    where anot/2 = 1/T integrated from -T/2 to T/2 f(t)dt, anot=pi

    The book answer has pi/2- [4/pi *the sum from n=1 to inf (1/(2n-1)^2*COS(2n-1)t

    Can anyone tell me if I basically have the same thing?

    Thanks.
     
  2. jcsd
  3. Dec 4, 2011 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, they are not at all the same thing. Your sum has cos(nt) for all n. The second sum only odd integers times t.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help With Fourier Series Expansion of a Periodic Function
Loading...