Fourier Transform of Rect fn

  • Thread starter mr_whisk
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  • #1
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Main Question or Discussion Point

Hi all,

How is the fourier transform applied to non-periodic functions, such as the Rect function?

Any help would be greatly appreciated,

Cheers,

Jamie :)
 

Answers and Replies

  • #2
mathman
Science Advisor
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I think you are confusing Fourier series, which apply to periodic functions, and Fourier transforms, which apply to integrable (in some sense) functions.
 
  • #3
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OK, i can see why my post appeared to sound like that, but I know what the differnce is.

What i mean is, say, how would you show that the FT transform of {1} is a delta function??

Cheers
 
  • #4
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Let A be a ( large ) positive real number

The transform you specified will lead you to integrate exp( - i * w * t ) with t ranging from -A to A, and letting A approaching +∞. When A approaches +∞, this will give you a function similar to one of these :

http://en.wikipedia.org/wiki/Impulse_function#Representations_of_the_delta_function

I let you try the computation and identify which one corresponds to the Fourier transform of 1.
 

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