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!

Fourier Series

  1. Apr 3, 2009 #1
    Find the fourier expansion of one period of f(t)=1+t absolute value of t<1

    I found this to be 1+2/pi Sigma(0 to infinity) ((-1^(n+1))/n)sinnpit by just the standard methods of the a0 an and bn formuals, which I know is correct

    Now the parts I am having problems with is part b and c which our teacher has not covered much at all and I cannot find any help online.

    Part b. Use the fourier expansion of f to find the sum of the Series
    Sigma(0toinfinity)(-1^n)/(2n+1)

    Part C. If f denotes the function defined on (-infinity to infinity) by the fourier series of f, find F(1)+F(-5)-3F(0)
     
  2. jcsd
  3. Apr 3, 2009 #2
    Just to make things a bit more clear on the notation side, I take it your expansion is:

    [tex]1+\frac{2}{\pi}\sum_{n=0}^{\infty}\frac{(-1)^{n+1}}{n} \sin{n\pi t}[/tex]

    As for question b:

    Notice that if you set t equal to [tex]t_0 \equiv \frac{1}{2}[/tex], then

    [tex]\sin{n\pi t_0} = \sin{\frac{n\pi}{2}}[/tex]

    which is zero whenever n is even and [tex](-1)^{(n-1)/2[/tex] whenever n is odd.... Do you see where I'm going with this?

    part C:
    I take it by F(0) you just mean f(0)? Have you tried filling in these numbers into the fourier series?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fourier Series
  1. Fourier Series (Replies: 1)

  2. Fourier series (Replies: 10)

  3. Fourier Series (Replies: 1)

  4. Fourier Series (Replies: 6)

Loading...