Engineering Tables/Fourier Transform Table 2

Signal Fourier transform unitary, angular frequency Fourier transform unitary, ordinary frequency Remarks 10The rectangular pulse and the normalized sinc function 11Dual 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. 14Shows 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