# 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.

• Well then something about your vector manipulation or division is wrong. A common trap in Matlab is that the ' operator and .' operator are different. The first is conjugate transpose while the second is just transpose. – Andy Walls Jul 22 at 9:55
• I would be easier for us if you could include your matlab code. – AlexTP Jul 22 at 10:04

$${{\hat {x}}(\nu )=\int _{-\infty }^{+\infty }x(t)\,\mathrm {e} ^{-2{\rm {i}}\pi\nu t}\,\mathrm {d} t}.$$
Are you sure you didn't forget the minus (-) sign in the exponential ? In this case, because $$x(t)$$ is real, You will effectively find the conjugate of $${\hat {x}}(\nu )$$ at the end.