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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.

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    $\begingroup$ 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. $\endgroup$
    – Andy Walls
    Commented Jul 22, 2020 at 9:55
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    $\begingroup$ I would be easier for us if you could include your matlab code. $\endgroup$
    – AlexTP
    Commented Jul 22, 2020 at 10:04

2 Answers 2

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

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If we assume that the Fourrier Transform formula is :

$${{\hat {x}}(\nu )=\int _{-\infty }^{+\infty }x(t)\,\mathrm {e} ^{-2{\rm {i}}\pi\nu t}\,\mathrm {d} t}.$$

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.

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  • $\begingroup$ Please check my updated question. I used Matlab fft function so there is no way the fft itself is wrong. $\endgroup$
    – 7E10FC9A
    Commented Jul 22, 2020 at 9:14

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