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Sketch the form of the Fourier transform - is this right?

  1. Oct 18, 2012 #1
    "Sketch the form of the Fourier transform" - is this right?

    Question ~ sketch the "form of the Fourier transform" for the function:

    f(k) = sin^2(ka/2) / (ka/2)^2


    So I'm thinking it will look like a cos [or sin] graph (shifted so that its 'above' *f(k)=0*) and that there will be some sort of *central* highest maximum and then the hight of the peaks tends to 0.

    *** My question is does this graph have one highest maximum when k=0 or does it have two highest maximums either side of the origin spaced evenly from the origin [k=0]?

    At the moment I'm thinking there will be two highest maximums which occur at -π/2 and π/2. Also, that when k = 0, f(k)=0.

    Later on however in the question it implies that there is one central maximum:

    "...find the values of k when f(k) first becomes zero either side of the central maximum at k=0..."


    Any advice?
     
  2. jcsd
  3. Oct 18, 2012 #2
    Re: "Sketch the form of the Fourier transform" - is this right?

    There is a concept called the sinc function.

    [itex]sin(k/2)/(k/2) = sinc(k/2)[/itex]

    The function has one maximum at k=0, and is symmetric across k = 0. You function is the square version of this function, when the variable is taken to be ka/2.
     
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