Results 1 to 7 of 7

Math Help - Fourier Coefficients

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    15

    Fourier Coefficients

    Find the Fourier coefficients of the piecewise continuousfunction


    f(t) = {0 if t <= (less than or equal to) 0 or 1 if t > 0.}


    I get why Ck is equal to 0. But why is Bk = 2/(k(pi)) when k is odd. And why is A0 = 1/(root(2)). Thanks for any help.

    (sorry its written in straight text)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by smellatron View Post
    Find the Fourier coefficients of the piecewise continuousfunction


    f(t) = 0 if t <= (less than or equal to) 0
    1 if t > 0.


    I get why Ck is equal to 0. But why is Bk = 2/(k(pi)) when k is odd. And why is A0 = 1/(root(2)). Thanks for any help.

    (sorry its written in straight text)
    You didn't specify an interval, but I'm guessing you want it on [-\pi,\pi]

    By definition a_0=\frac{1}{\pi} \int_{-\pi}^{\pi}f(t)dt = \frac{1}{\pi} \int_{-\pi}^{0} 0 dt + \frac{1}{\pi} \int_{0}^{\pi}1dt =1

    a_n=\frac{1}{\pi}\int_{0}^{\pi}\cos(nt)dt=\frac{\s  in(nt)}{n}\bigg|_{0}^{\pi}=\frac{\sin(\pi n)}{n}=0

    b_n=\frac{1}{\pi}\int_{0}^{\pi}\sin(nt)dt=-\frac{\cos(nt)}{n}\bigg|_{0}^{\pi}=-\frac{1}{\pi n}(\cos(\pi n)-1)=-\frac{1}{\pi n}[(-1)^n-1]

    note that when ever n is even b_n=0 so it can be rewritten as follows

    b_n=\frac{2}{(2n-1) \pi } for n=1,2,3...

    so we get

    f(t) \approx \frac{1}{2} +\frac{2}{\pi}\sum_{n=1}^{\infty}\frac{\sin[(2n-1)t]}{2n-1}
    Last edited by TheEmptySet; March 30th 2009 at 07:19 PM. Reason: lost minus sign
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    15
    I have A0 equal to 1/(root(2)). That is still goofing me up.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by smellatron View Post
    I have A0 equal to 1/(root(2)). That is still goofing me up.
    How did you cacluate it?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Fourier Coefficients-capture.jpg

    Here is an immage. \frac{1}{\sqrt{2}} version is in blue and does not fit the function described.

    the 1/2 fits very nicely.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Feb 2009
    Posts
    15
    That is the answer in the back of the book. I was just confused on how they came up with A0. Are you saying that the answer in the book is possibly wrong? Thanks you for your help.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by smellatron View Post
    That is the answer in the back of the book. I was just confused on how they came up with A0. Are you saying that the answer in the book is possibly wrong? Thanks you for your help.
    I disagree with the back of your book, but you still didn't answer my question how did you calculate it. When you try to calclucate it what do you get...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fourier Coefficients
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 10th 2011, 06:34 AM
  2. Fourier Coefficients?
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: May 29th 2010, 07:43 AM
  3. Fourier coefficients
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 7th 2010, 11:36 PM
  4. Fourier coefficients
    Posted in the Advanced Math Topics Forum
    Replies: 10
    Last Post: December 31st 2008, 03:05 PM
  5. fourier coefficients
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 23rd 2008, 07:47 AM

Search Tags


/mathhelpforum @mathhelpforum