\[f(x)=\frac{1}{\pi}\int_{-\infty}^{\infty}\left(\int_{0}^{\infty}\cos\left(xt%
\right)\cos\left(yt\right)\,\mathrm{d}t\right)f(y)\,\mathrm{d}y+\frac{1}{\pi}%
\int_{-\infty}^{\infty}\left(\int_{0}^{\infty}\sin\left(xt\right)\sin\left(yt%
\right)\,\mathrm{d}t\right)f(y)\,\mathrm{d}y,\]