how I measure the phase btween two signals in frquencie domain

Started by June 24, 2005
Hi,
I have two signals
s1(t)=sin(w*t)
s2(t)=sin(w*t+phi),
I want to measure phi in frequencie domain.
I know some technics in temporal domain like cross correlation, ....
please can you help me to find method to calculate the phase phi in
frequencie domain.

thank you.

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relative phase = arctan((sin(w*t)*sin(w*t+phi))/(sin(w*t)*cos(w*t+phi)))

"signal" <monirov@hotmail.com> wrote in message
news:BrGdnUyWv8ix_SHfRVn-jw@giganews.com...
> Hi, > I have two signals > s1(t)=sin(w*t) > s2(t)=sin(w*t+phi), > I want to measure phi in frequencie domain. > I know some technics in temporal domain like cross correlation, .... > please can you help me to find method to calculate the phase phi in > frequencie domain. > > thank you. > > > > This message was sent using the Comp.DSP web interface on > www.DSPRelated.com
"signal" <monirov@hotmail.com> wrote in message
news:BrGdnUyWv8ix_SHfRVn-jw@giganews.com...
> Hi, > I have two signals > s1(t)=sin(w*t) > s2(t)=sin(w*t+phi), > I want to measure phi in frequencie domain. > I know some technics in temporal domain like cross correlation, .... > please can you help me to find method to calculate the phase phi in > frequencie domain. >
Assuming that you have a reasonably long record, compute a Finite Fourier Transform of each. Each will have a peak amplitude at w. Each will have a phase value at w. Take the difference between the phase values. You may have to unwrap the phase to do this in a meaningful way.... that is, you may need to add k*2*pi radians to the phases (where k is an integer) in order to assure there are no "jumps" of 2*pi radians in the results you are working with. If you know w, then you might make the length of the finite time record an integer multiple of 1/w. I didn't mention sampling yet... If the time record is of N samples with sampling interval T, then the finite time record will be NT seconds long (assuming an interval of T seconds exists beyond the last sample). This will result in a Discrete Fourier Transform with frequency sample interval of 1/NT. You might like a frequency sample to occur at w. If so, you make w=k/NT and NT=k/w as above. Then the Finite, Discrete Fourier Transform will result in a frequency sample at exactly w. You might even compute just that one sample using the Goertzel algorithm or some such thing. Fred