I can not find the Fourier transform of Bartlett window

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The discussion centers on the Fourier transform of the Bartlett window, defined as w(t)=1-|t|/u for -u<t<u and w(t)=0 otherwise. The expected Fourier transform is given as W(f)=1/u*(sin(π*f*u)/(π*f))^2. A user reports successfully finding the transform for a rectangular window but struggles with the Bartlett window, ultimately deriving an alternative form: -1/4/u/π^2/f^2*((-1)^(-2*u*f)+(-1)^(2*u*f)-2). They confirm that this derived function is numerically equivalent to the expected result and seek clarification on how to derive one from the other. The conversation highlights the complexities involved in transforming the Bartlett window and the relationship between different forms of the Fourier transform.
truva
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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 couldn't find it in case of Bartlett window. Where am I wrong?
 
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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 )
 
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