Results 1 to 5 of 5

Math Help - Fourier Series of sinx

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    13

    Fourier Series of sinx

    Hi there,

    I'm slightly confused about something in a question on a past exam paper for my Fourier analysis module.

    I have a question were f(x) is sinx on the interval [0, pi], and f bar denotes the periodic extension with period pi of f.

    It asks me to sketch the graph of f bar, and show on the interval [-pi, pi] that f bar is even. I can do both of these. It then asks me to calculate the trigonometric Fourier series of f. I'm just not sure which interval it wants me to use, that with the extention or without. Also, can I ignore the an cosnx part of the Fourier Series formula as I know I am calculating for sinnx? The first couple of lines of the calculation would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    The period of function is \pi and You have to compute the coefficients a_{n} and b_{n} as...

    a_{n} = \frac{2}{\pi} \int_{0}^{\pi} \sin x\cdot \cos 2 n x \cdot dx

    b_{n} = \frac{2}{\pi} \int_{0}^{\pi} \sin x\cdot \sin 2 n x \cdot dx (1)

    The periodoc function will be expressed as...

    f(x) = \frac{a_{0}}{2} + \sum_{n=1}^{\infty} (a_{n} \cos 2 n x + b_{n} \sin 2 n x) (2)

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    13
    So, when it asks me for the trigonometric fourier series, is this a different question to if it asked for the Fourier cosine series or the Fourier sine series? Does the fact that the periodic extension on [0, pi] is even mean I just need the Fourier cosine series?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2010
    Posts
    2
    ok, I'm only a student myself but so I could be wrong, I don't understand why you are saying sin is even, sin is an odd function, such that f(-x)=-f(x). However your bn term would be even, it's an odd function by an odd function. I don't know if that helps you. this way you can use the interval of integration 0 to pi. if you multiply by 2...
    I hope this helps.
    and yes, "Also, can I ignore the an cosnx part of the Fourier Series formula as I know I am calculating for sinnx?" you can 'ignore' the cosnx part.... this is because when the function is odd An is equal to Zero.

    I have a question though...
    "Show on the interval [-pi, pi] that f bar is even." why is this so?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2010
    Posts
    2
    Sorry, ignore my question I didn't read it right! and I'm sorry I can't help you with which interval to use....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex Fourier Series & Full Fourier Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 9th 2009, 05:39 AM
  2. taylor series expansion of exp^sinx
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 4th 2009, 01:51 PM
  3. Fourier Series for f(x)= abs(sinx)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 2nd 2008, 03:01 PM
  4. from fourier transform to fourier series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 1st 2008, 06:35 AM
  5. Fourier series of sinx
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 4th 2007, 06:36 PM

Search Tags


/mathhelpforum @mathhelpforum