# 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

```