Definition:Inverse Fourier Transform/Real Function/Also known as

Inverse Fourier Transform of Real Function: Also known as

The real inverse Fourier transform function is sometimes referred to as the plus-$i$ transform of $\map F s$.

This allows us to distinguish between this and the real Fourier transform function, known in turn as the minus-$i$ transform of $\map f t$.

Ronald N. Bracewell, in his The Fourier Transform and its Applications, 2nd ed. of $1978$, discusses all $3$ of the formulations given in $\mathsf{Pr} \infty \mathsf{fWiki}$, referring to them as System $1$, System $2$ and System $3$.

The numbers assigned to Formulation $1$, Formulation $2$ and Formulation $3$ have been configured so as to correspond to these directly.

Sources

• 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Chapter $2$: Groundwork: The Fourier transform and Fourier's integral theorem