Engineering Tables/Fourier Transform Table 2
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Signal  Fourier transform unitary, angular frequency 
Fourier transform unitary, ordinary frequency 
Remarks  

10  The rectangular pulse and the normalized sinc function  
11  Dual of rule 10. The rectangular function is an idealized lowpass filter, and the sinc function is the noncausal impulse response of such a filter.  
12  tri is the triangular function  
13  Dual of rule 12.  
14  Shows that the Gaussian function is its own Fourier transform. For this to be integrable we must have .  
common in optics  
a>0  
the transform is the function itself  
J_{0}(t) is the Bessel function of first kind of order 0, rect is the rectangular function  
it's the generalization of the previous transform; T_{n} (t) is the Chebyshev polynomial of the first kind.  


U_{n} (t) is the Chebyshev polynomial of the second kind 