Fourier transform of sin²(ka/2)/(ka/2)²: central vs symmetric maxima

[Zomboy]

"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)^2So 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 height 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?

 

[MisterX]

There is a concept called the sinc function.

$sin(k/2)/(k/2) = sinc(k/2)$

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.