# [SOLVED]Fast Fourier Transform and its inverse

#### dwsmith

##### Well-known member
Does every FFT have $$i$$ in it?

Given $$u_t = -(u_{xxx} + 6uu_x)$$.

$$f'''(x) = \mathcal{F}^{-1}\left[(ik)^3\mathcal{F}(f(x))\right]$$
$$f'(x) = \mathcal{F}^{-1}\left[(ik)\mathcal{F}(f(x))\right]$$

The only equation I have used the pseudo-spectral method on was the NLS which is
$$u_t = i(u_{xx} + |u|^2u)$$. In this case, I know I will have $$i$$ in the FFT.

Are my transforms for the KdV correct or do I need to remove $$i$$?