\[|\mathcal{F}\left(x\right)|^{2}=2+{\mathrm{f}}^{2}\left(-x\right)+{\mathrm{g}}%
^{2}\left(-x\right)-2\sqrt{2}\cos\left(\tfrac{1}{4}\pi+\tfrac{1}{2}\pi x^{2}%
\right)\mathrm{f}\left(-x\right)-2\sqrt{2}\cos\left(\tfrac{1}{4}\pi-\tfrac{1}{%
2}\pi x^{2}\right)\mathrm{g}\left(-x\right),\]