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: Foorier represtaion of this function

  1. Dec 23, 2009 #1
    [tex]f(x)=\sin(\frac{px}{2})\\[/tex]

    [tex]a_0=0[/tex]

    [tex]a_n=0[/tex]

    [tex]b_n=\frac{1}{\pi}\int_{-\pi}^{\pi}\(\sin(\frac{px}{2}))\sin(nx)dx=\frac{1}{2\pi}[\sin(\frac{p\pi}{2}-n\pi)-\sin(\frac{-p\pi}{2}+n\pi)]+\frac{1}{2\pi}[\sin(\frac{p\pi}{2}+n\pi)-\sin(\frac{-p\pi}{2}-n\pi)][/tex]




    i used trig identetied to splt into two cosines

    andi solved

    but i got sines

    i need an expression of cosines to do cos nx=(-1)^n



    i need to have a simple linear fracture without cosines or sines



    i cant transform it here in the needed form

    ?

    and if thinking thurely then i see that i have a trig function on a simetric period
    so its zero

    so the foorier representation of the given function is zero
    ?

    where is the mistake
    it cant be zero
     
  2. jcsd
  3. Dec 23, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi nhrock3! :smile:

    These trigonometric identities need a factor of 1/2 inside the RHS brackets. :wink:
     
  4. Dec 23, 2009 #3
    i took the 0.5 out side of the integral
     
  5. Dec 23, 2009 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    i'm getting confused :redface:

    let's start again … shouldn't there be factors of 1/(p/2 ± n) after the integration?
     
  6. Dec 23, 2009 #5

    whs

    User Avatar

    foorier... Really? Did you really just do that? I'd attempt a response but I can't read whatever the hell you typed.
     
  7. Dec 24, 2009 #6

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You need to state your problem more clearly. Are you trying to find a Fourier series that represents your function for all x? If not that, on what interval? Why are you choosing [itex](-\pi,\pi)[/itex]? Depending on the value of p, the periodic extension of your function from that interval may have discontinuities. Do your care about that? Do you want a half range expansion? A more careful statement of the problem please.

    And what is "a simple linear fracture without sines or cosines?"
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook