Phase difference from cross power spectrum

Hi all,

I heard we can obtain the phase difference between two signal from
cross power spectrum.
If someone knew, could you show me how to obtain the phase difference ?
I mean the algorithm.
I read the cross power spectrum is defined as FFT (A) FFT*(B) / N^2, so
we have real and imaginary components.

Thanks,
Titi

Ordinary student skrev:
> Hi all,
>
> I heard we can obtain the phase difference between two signal from
> cross power spectrum.
> If someone knew, could you show me how to obtain the phase difference ?
> I mean the algorithm.
> I read the cross power spectrum is defined as FFT (A) FFT*(B) / N^2, so
> we have real and imaginary components.

Do you know about the polar form of complex numbers?

Rune

Rune Allnor wrote:
> Ordinary student skrev:
> > Hi all,
> >
> > I heard we can obtain the phase difference between two signal from
> > cross power spectrum.
> > If someone knew, could you show me how to obtain the phase difference ?
> > I mean the algorithm.
> > I read the cross power spectrum is defined as FFT (A) FFT*(B) / N^2, so
> > we have real and imaginary components.
>
> Do you know about the polar form of complex numbers?
>
> Rune

Yes.
If I am not wrong, for example we have x+iy
then we can write it as r cos (theta) + i r sin (theta),
r^2 = (x^2 + y^2)
arctan(theta) = y/x

Titi

Ordinary student skrev:
> Rune Allnor wrote:
> > Ordinary student skrev:
> > > Hi all,
> > >
> > > I heard we can obtain the phase difference between two signal from
> > > cross power spectrum.
> > > If someone knew, could you show me how to obtain the phase difference ?
> > > I mean the algorithm.
> > > I read the cross power spectrum is defined as FFT (A) FFT*(B) / N^2, so
> > > we have real and imaginary components.
> >
> > Do you know about the polar form of complex numbers?
> >
> > Rune
>
> Yes.
> If I am not wrong, for example we have x+iy
> then we can write it as r cos (theta) + i r sin (theta),
> r^2 = (x^2 + y^2)

Right

> arctan(theta) = y/x

Wrong. I am sure you spot the flaw if you take a second to
look the expression over once more. After correcting it, the
phase angle theta is computed as...?

Rune

Rune Allnor wrote:
> Ordinary student skrev:
> > Rune Allnor wrote:
> > > Ordinary student skrev:
> > > > Hi all,
> > > >
> > > > I heard we can obtain the phase difference between two signal from
> > > > cross power spectrum.
> > > > If someone knew, could you show me how to obtain the phase difference ?
> > > > I mean the algorithm.
> > > > I read the cross power spectrum is defined as FFT (A) FFT*(B) / N^2, so
> > > > we have real and imaginary components.
> > >
> > > Do you know about the polar form of complex numbers?
> > >
> > > Rune
> >
> > Yes.
> > If I am not wrong, for example we have x+iy
> > then we can write it as r cos (theta) + i r sin (theta),
> > r^2 = (x^2 + y^2)
>
> Right
>
> > arctan(theta) = y/x
>
> Wrong. I am sure you spot the flaw if you take a second to
> look the expression over once more. After correcting it, the
> phase angle theta is computed as...?
>
> Rune

Sorry lol,
phase = arctan(y/x),
this equation equals to phase spectrum in radians.

Titi