I can not find the Fourier transform of Bartlett window

1. Dec 11, 2011

truva

For the Bartlett window below:

w(t)=1-|t|/u for -u<t<u
w(t)=0 otherwise

the books say that the fourier transform of it is
W(f)=1/u*(sin(∏*f*u)/(pi*f))

I use symbolic toolbox of matlab and can find the transform of a rectangular window. But I couldnt find it in case of Bartlett window. Where am I wrong?

2. Dec 12, 2011

truva

I just realized that I had find the result, but in a different form as the following:

-1/4/u/pi^2/f^2*((-1)^(-2*u*f)+(-1)^(2*u*f)-2)

And I checked it numerically that the function is exactly equal to the function below:

u*(sin(pi*u*f)/u/pi/f)^2

I am not a mathematician and it is not necessary for me but I am wondering: How can I derive the second function from the first one?

( NOTE: in the first post, there is a typing error. It should be W(f)=1/u*(sin(∏*f*u)/(pi*f))^2 )

Last edited: Dec 12, 2011
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