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Fourier transform unitary, angular frequency |
Fourier transform unitary, ordinary frequency |
Remarks
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10
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The rectangular pulse and the normalized sinc function
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11
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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.
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12
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tri is the triangular function
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13
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Dual of rule 12.
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14
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Shows that the Gaussian function is its own Fourier transform. For this to be integrable we must have .
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common in optics
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a>0
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the transform is the function itself
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J0(t) is the Bessel function of first kind of order 0, rect is the rectangular function
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it's the generalization of the previous transform; Tn (t) is the Chebyshev polynomial of the first kind.
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Un (t) is the Chebyshev polynomial of the second kind
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