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For question related to Fourier transforms.

The Fourier transform of a function $f(t)$ is denoted by $\hat f(x)$ and is defined as

$$\hat f(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} f(t)e^{-2\pi itx} dt$$

The inverse Fourier transform is defined as

$$f(t)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} \hat f(x)e^{2\pi itx} dx$$