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Fourier Series for a Square-wave Function

  1. Dec 10, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider the square wave function defined by y(t) = h (constant) when 0 ≤ (t + nT) ≤1,
    y(t) = 0 elsewhere, where T = 2 is the period of the function. Determine the Fourier series
    expansion for y(t).

    2. Relevant equations

    Fourier Analysis Coefficients

    3. The attempt at a solution

    Please look at the attachment, I am not convinced I have done it right so far... please help.
     

    Attached Files:

  2. jcsd
  3. Dec 10, 2013 #2

    jbunniii

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    Your answer for ##A_n## can be simplified. Since ##T=2##, it becomes
    $$A_n = \frac{h}{\pi n} \sin(\pi n)$$
    Now what is ##\sin(\pi n)##?
     
  4. Dec 10, 2013 #3

    jbunniii

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    By the way, you can save yourself some work as follows. Note that if we define ##x(t) = y(t) - h/2##, then ##x## is an odd function. What can you say about the Fourier series of an odd function? And how does the Fourier series of ##x## relate to the Fourier series of ##y##?
     
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