f(x)=\frac{1}{\pi}\int^{\infty}_{0}du\int^{\infty}_{-\infty}f(\xi)cosu(x-\xi)d\xi=\frac{1}{\pi}\int^{\infty}_{-\infty}f(\xi)d\xi\int^{\infty}_{0}cosu(x-\xi)du