How Is the Fourier Transform Applied to the Rect Function?

[mr_whisk]

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 :)

 

[mathman]

I think you are confusing Fourier series, which apply to periodic functions, and Fourier transforms, which apply to integrable (in some sense) functions.

 

[mr_whisk]

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

 

[deiki]

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.