I can not find the Fourier transform of Bartlett window

Click For Summary
SUMMARY

The Fourier transform of the Bartlett window, defined as w(t)=1-|t|/u for -u PREREQUISITES

  • Understanding of Fourier transforms
  • Familiarity with the Bartlett window function
  • Experience using MATLAB's symbolic toolbox
  • Basic knowledge of trigonometric identities
NEXT STEPS
  • Study the derivation of the Fourier transform for different window functions
  • Learn how to use MATLAB for symbolic mathematics
  • Explore the properties of the Bartlett window in signal processing
  • Investigate numerical verification techniques for Fourier transforms
USEFUL FOR

Signal processing engineers, MATLAB users, and students studying Fourier analysis will benefit from this discussion, particularly those interested in window functions and their transforms.

truva
Messages
18
Reaction score
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?
 
Physics news on Phys.org
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:

Similar threads

  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 17 ·
Replies
17
Views
3K