Phase of FFT compared to phase of Sinusoid

Hi everyone,

I'm generating a sinusoid of the form cos(wt + phi), then taking the
FFT.

I was expecting to find the phase of the FFT (at the frequency peak)
allows me to determine 'phi' in the generating sinusoid, but there
appears to be little correlation!

For example,

plotting cos(2 Pi x/10) from x=0 to 2million (with step 1) , the phase
at the FFT is 2.82?!! Surely the phase should be zero since the inital
phase at x=0 was zero?

Thanks for your help!


Peter Moreton

peter.moreton@gmail.com wrote:
> Hi everyone,
> 
> I'm generating a sinusoid of the form cos(wt + phi), then taking the
> FFT.
> 
> I was expecting to find the phase of the FFT (at the frequency peak)
> allows me to determine 'phi' in the generating sinusoid, but there
> appears to be little correlation!
> 
> For example,
> 
> plotting cos(2 Pi x/10) from x=0 to 2million (with step 1) , the phase
> at the FFT is 2.82?!! Surely the phase should be zero since the inital
> phase at x=0 was zero?
> 
> Thanks for your help!
> 
> 
> Peter Moreton
> 

So you're saying you took a 2 million point FFT? I have my doubts about 
this. Could you describe exactly what you did.

Cheers,
David

<peter.moreton@gmail.com> wrote in message 
news:1142941236.513153.267210@j33g2000cwa.googlegroups.com...
> Hi everyone,
>
> I'm generating a sinusoid of the form cos(wt + phi), then taking the
> FFT.
>
> I was expecting to find the phase of the FFT (at the frequency peak)
> allows me to determine 'phi' in the generating sinusoid, but there
> appears to be little correlation!
>
> For example,
>
> plotting cos(2 Pi x/10) from x=0 to 2million (with step 1) , the phase
> at the FFT is 2.82?!! Surely the phase should be zero since the inital
> phase at x=0 was zero?
>
That's odd -what do you get if you fft(cos(2 Pi x/16)) with x=0 to 15 ?

best of luck - Mike

Thanks guys, I have worked out the problem.

When i did  fft(cos(2 Pi x/16)) with x=0 to 15, the phase was correct.

My problem was coming from the fact that my frequency was not an
integer number of wavelengths over the range.

This gives spectral leakage into neighbouring bins and the phase is no
longer correct.

But say the corrrect frequency is at f =15.125, and there is a pi phase
jump between 15 and 16. If i interpolate the phase by doing 0.125 x pi=
0.393, then add the phase i would expect(phi), this gives the correct
phase!


Thanks for your help Mike, sometimes i forget the best advise is keep
it simple!

Cheers,


Peter

Thanks guys, I have worked out the problem.

When i did  fft(cos(2 Pi x/16)) with x=0 to 15, the phase was correct.

My problem was coming from the fact that my frequency was not an
integer number of wavelengths over the range.

This gives spectral leakage into neighbouring bins and the phase is no
longer correct.

But say the corrrect frequency is at f =15.125, and there is a pi phase
jump between 15 and 16. If i interpolate the phase by doing 0.125 x pi=
0.393, then add the phase i would expect(phi), this gives the correct
phase!


Thanks for your help Mike, sometimes i forget the best advise is keep
it simple!

Cheers,


Peter

Thanks guys, I have worked out the problem.

When i did  fft(cos(2 Pi x/16)) with x=0 to 15, the phase was correct.

My problem was coming from the fact that my frequency was not an
integer number of wavelengths over the range.

This gives spectral leakage into neighbouring bins and the phase is no
longer correct.

But say the corrrect frequency is at f =15.125, and there is a pi phase
jump between 15 and 16. If i interpolate the phase by doing 0.125 x pi=
0.393, then add the phase i would expect(phi), this gives the correct
phase!


Thanks for your help Mike, sometimes i forget the best advise is keep
it simple!

Cheers,


Peter

Thanks guys, I have worked out the problem.

When i did  fft(cos(2 Pi x/16)) with x=0 to 15, the phase was correct.

My problem was coming from the fact that my frequency was not an
integer number of wavelengths over the range.

This gives spectral leakage into neighbouring bins and the phase is no
longer correct.

But say the corrrect frequency is at f =15.125, and there is a pi phase
jump between 15 and 16. If i interpolate the phase by doing 0.125 x pi=
0.393, then add the phase i would expect(phi), this gives the correct
phase!


Thanks for your help Mike, sometimes i forget the best advise is keep
it simple!

Cheers,


Peter

Thanks guys, I have worked out the problem.

When i did  fft(cos(2 Pi x/16)) with x=0 to 15, the phase was correct.

My problem was coming from the fact that my frequency was not an
integer number of wavelengths over the range.

This gives spectral leakage into neighbouring bins and the phase is no
longer correct.

But say the corrrect frequency is at f =15.125, and there is a pi phase
jump between 15 and 16. If i interpolate the phase by doing 0.125 x pi=
0.393, then add the phase i would expect(phi), this gives the correct
phase!


Thanks for your help Mike, sometimes i forget the best advise is keep
it simple!

Cheers,


Peter

Thanks guys, I have worked out the problem.

When i did  fft(cos(2 Pi x/16)) with x=0 to 15, the phase was correct.

My problem was coming from the fact that my frequency was not an
integer number of wavelengths over the range.

This gives spectral leakage into neighbouring bins and the phase is no
longer correct.

But say the corrrect frequency is at f =15.125, and there is a pi phase
jump between 15 and 16. If i interpolate the phase by doing 0.125 x pi=
0.393, then add the phase i would expect(phi), this gives the correct
phase!


Thanks for your help Mike, sometimes i forget the best advise is keep
it simple!

Cheers,


Peter

Thanks guys, I have worked out the problem.

When i did  fft(cos(2 Pi x/16)) with x=0 to 15, the phase was correct.

My problem was coming from the fact that my frequency was not an
integer number of wavelengths over the range.

This gives spectral leakage into neighbouring bins and the phase is no
longer correct.

But say the corrrect frequency is at f =15.125, and there is a pi phase
jump between 15 and 16. If i interpolate the phase by doing 0.125 x pi=
0.393, then add the phase i would expect(phi), this gives the correct
phase!


Thanks for your help Mike, sometimes i forget the best advise is keep
it simple!

Cheers,


Peter