I can not find the Fourier transform of Bartlett window

In summary, the conversation discusses the Fourier transform of a Bartlett window and the different forms it can be derived in. The first form is given as W(f)=1/u*(sin(∏*f*u)/(pi*f)) while the second form is u*(sin(pi*u*f)/u/pi/f)^2. The speaker also mentions using the symbolic toolbox of MATLAB to find the transform and wondering how the second function can be derived from the first one.
  • #1
truva
18
1
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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  • #2
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:

Related to I can not find the Fourier transform of Bartlett window

What is the Fourier transform of a Bartlett window?

The Fourier transform of a Bartlett window is a triangular function that represents the frequency content of the signal.

Why is it difficult to find the Fourier transform of a Bartlett window?

It can be difficult to find the Fourier transform of a Bartlett window because it involves a complex mathematical calculation and may require advanced knowledge of signal processing and Fourier analysis.

Can the Fourier transform of a Bartlett window be calculated analytically?

Yes, the Fourier transform of a Bartlett window can be calculated analytically using mathematical equations and formulas. However, it may be challenging for those who are not familiar with these concepts.

What are some alternative ways to find the Fourier transform of a Bartlett window?

One alternative method is to use a computer program or software that is specifically designed to calculate Fourier transforms. Another option is to approximate the Fourier transform using numerical methods such as the discrete Fourier transform.

Why is the Fourier transform of a Bartlett window important in signal processing?

The Fourier transform of a Bartlett window is important in signal processing because it helps to analyze the frequency content of a signal and can be used to filter out unwanted noise or extract useful information from the signal.

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