Temporal Fourier transform / inverse:
Spatial Fourier transform / inverse:
where D is the distance between the planes containing f(x) and F(x).
Generalization of Parseval’s Theorem (Cross-Product Theorem):
where f(x) is a spatial function, F(α) is its Fourier transform, and F(ξ) is its Fresnel transform.
Sifting property of the delta function:
The sifting property also applies to a sine function of the form sinc(2αcox):
provided that f(x) is bandlimited to αco and that αm ≥ αco.
Other useful relationships: ...