What could cause fast Fourier transform to give complex conjugate of the intended result?

I have 2 real time series $x(t)$ and $y(t)$, after fft it should become $tilde{X}(f)$ and $tilde{Y}(f)$. Then I need to normalize $tilde{X}(f)$ with $tilde{Y}(f)$ : $tilde{X}(f)/tilde{Y}(f)=tilde{Z}(f)$

However fft gives me $tilde{Z}^*(f)$ instead (the sign of the imaginary part is inverted).

What could have caused this ? I know $x(-t)$ and $y(-t)$ can cause $tilde{Z}^*(f)$, but $x(t)$ and $y(t)$ have the correct physical meaning.