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.
Taking the inverse FFT (IFFT) instead of FFT would cause a phase inversion.