Connes Function

The Apodization Function

$$A(x)=\left({1-{x^2\over a^2}}\right)^2.$$

Its Full Width at Half Maximum is $\sqrt{4-2\sqrt{2}}\,a$, and its Instrument Function is

$$I(x)=8a\sqrt{2\pi}\, {J_{5/2}(2\pi ka)\over (2\pi ka)^{5/2}},$$

where $J_n(z)$ is a Bessel Function of the First Kind.

See also Apodization Function