Thread Subject: Ortogonality prinsiple for noised sine vawes: solving amplitude and phase of sine vawe when frequency is known

Hi,

is there any ready functions in matlab which solves amplitudes and phase of sine vawe when frequency is known. For example, in

https://noppa.tkk.fi/noppa/kurssi/t-61.3040/viikkoharjoitukset

exercise 24.9. problem 5 uses this method. (Click "Problem set in English" )

Exercise starts as :

You have observed the values x(0); x(1); x(2) from the real-valued sinusoidal signal
x(n) = Asin(nw+a) + v(n); where v(n) is the noise term and a phase. Find the
amplitude A and the phase that minimize the squared error...

Thanks already for your answers/follow up-questions!

On Oct 6, 9:32 pm, "juho salminen" <jssal...@cc.hut.fi> wrote:
> Hi,
>
> is there any ready functions in matlab which solves amplitudes and phase of sine vawe when frequency is known. For example, in
>
> https://noppa.tkk.fi/noppa/kurssi/t-61.3040/viikkoharjoitukset
>
> exercise 24.9. problem 5 uses this method. (Click "Problem set in English" )
>
> Exercise starts as :
>
> You have observed the values x(0); x(1); x(2) from the real-valued sinusoidal signal
> x(n) = Asin(nw+a) + v(n); where v(n) is the noise term and a phase. Find the
> amplitude A and the phase that minimize the squared error...
>
> Thanks already for your answers/follow up-questions!

No, but you can derive it pretty easily.
First, use trig identities to expand the equation into a sin and cos
Next, go:
help mldivide

BTW, just to be pedantic, it's wave, not vawe.

On 6 Okt, 10:32, "juho salminen" <jssal...@cc.hut.fi> wrote:
> Hi,
>
> is there any ready functions in matlab which solves amplitudes and phase of sine vawe when frequency is known.

If there is exactly one sinusoidal with *known* frequency,
use DOT. If there are more sinusoidals amd/or the frequencies
are unknown, things become quite a bit more cumbersome.

Rune

Rune Allnor <allnor@tele.ntnu.no> wrote in message <82d70f61-0aff-40c6-909e-90f7995b87e2@m18g2000vbs.googlegroups.com>...
> On 6 Okt, 10:32, "juho salminen" <jssal...@cc.hut.fi> wrote:
> > Hi,
> >
> > is there any ready functions in matlab which solves amplitudes and phase of sine vawe when frequency is known.
>
> If there is exactly one sinusoidal with *known* frequency,
> use DOT. If there are more sinusoidals amd/or the frequencies
> are unknown, things become quite a bit more cumbersome.
>
> Rune

If there is only one sampled sinusoidal, you may use the function sinfapm from
http://www.mathworks.com/matlabcentral/fileexchange/19902
even in case that the frequency is not known exactly.
Mira

"Miroslav Balda" <balda.remove.this@cdm.cas.cz> wrote in message <hafl5v$c9k$1@fred.mathworks.com>...
> Rune Allnor <allnor@tele.ntnu.no> wrote in message <82d70f61-0aff-40c6-909e-90f7995b87e2@m18g2000vbs.googlegroups.com>...
> > On 6 Okt, 10:32, "juho salminen" <jssal...@cc.hut.fi> wrote:
> > > Hi,
> > >
> > > is there any ready functions in matlab which solves amplitudes and phase of sine vawe when frequency is known.
> >
> > If there is exactly one sinusoidal with *known* frequency,
> > use DOT. If there are more sinusoidals amd/or the frequencies
> > are unknown, things become quite a bit more cumbersome.
> >
> > Rune
>
> If there is only one sampled sinusoidal, you may use the function sinfapm from
> http://www.mathworks.com/matlabcentral/fileexchange/19902
> even in case that the frequency is not known exactly.
> Mira

Thanks for your answer.
It seems this function is not effective for detecting amplitudes of noisy sine waves. Often it returns something completely different than original amplitude of noisy sine.