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 low-pass filter, and the sinc function is the non-causal 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
J0(t) is the Bessel function of first kind of order 0, rect is the rectangular function
it's the generalization of the previous transform; Tn (t) is the Chebyshev polynomial of the first kind.

 


 

Un (t) is the Chebyshev polynomial of the second kind