# freq and phase estimation

Started by April 20, 2004
```What is the most effective way to adaptive estimate freqs and phases of the
mixture (superposition) of the signals:

s_i(t) = cos(2*pi*f_i*t+p_i)+n_i(t) ,

where i=1,2, ..., N and n_i is additive gaussian noise.

Michal

```
```Michal Kvasnicka wrote:

> What is the most effective way to adaptive estimate freqs and phases of the
> mixture (superposition) of the signals:
>
> s_i(t) = cos(2*pi*f_i*t+p_i)+n_i(t) ,
>
> where i=1,2, ..., N and n_i is additive gaussian noise.
>
> Michal

Homework?

--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;

```
```No!!!!

I am looking for most suitable method for FPGA implementing. Speed of
convergence of the adaptive estimator and high frequency and phase
resolution is most important challenge.

I know, that there is a lot of methods but in this time I am not able to
evaluate its. So, this is a reason why I am asking for help.

Michal

"Jerry Avins" <jya@ieee.org> p&#2013265933;se v diskusn&#2013265933;m pr&#2013265933;spevku
news:4085748f\$0\$16471\$61fed72c@news.rcn.com...
> Michal Kvasnicka wrote:
>
> > What is the most effective way to adaptive estimate freqs and phases of
the
> > mixture (superposition) of the signals:
> >
> > s_i(t) = cos(2*pi*f_i*t+p_i)+n_i(t) ,
> >
> > where i=1,2, ..., N and n_i is additive gaussian noise.
> >
> > Michal
>
> Homework?
>
> --
> Engineering is the art of making what you want from things you can get.
> &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
>

```
```Jerry Avins <jya@ieee.org> wrote in message news:<4085748f\$0\$16471\$61fed72c@news.rcn.com>...
> Michal Kvasnicka wrote:
>
> > What is the most effective way to adaptive estimate freqs and phases of the
> > mixture (superposition) of the signals:
> >
> > s_i(t) = cos(2*pi*f_i*t+p_i)+n_i(t) ,
> >
> > where i=1,2, ..., N and n_i is additive gaussian noise.
> >
> > Michal
>
> Homework?

Probably not. Frequency estimation is one of the more difficult
practical analysis problems to work with. I have written a number
of posts about various flavours of MUSIC, and a couple of other
methods for frequency estimation. Once one starts to bring
in amplitude and phase estimates as well, things become very difficult.

Michal, for frequency estimation you should look at MUSIC and the
Tufts/Kumaresan Forward-Backward Linear Prediction method. These
techniques are designed for the "sum-of-sine" signals and some
(but not all) are restricted to regularly sampled data. You should
also take some time to read up on the Cramer-Raou Lower bound of
variance of parameter estimates. The problem is that there are
limits to how precise estimates of frequency and phase can be.

Rune
```
```Thanks. But the MUSIC like methods estimate only frequency. What about
simultaneous estimation of the frequency and phase? Do you know any suitable
method and combination of methods for this type of problem?

I know very well that C-R bound limitate the precision of the final freq and
phase estimation. But now I am looking for any suitable method for
simulataneous freq+phase estimation.

Michal
"Rune Allnor" <allnor@tele.ntnu.no> p&#2013265933;se v diskusn&#2013265933;m pr&#2013265933;spevku
> Jerry Avins <jya@ieee.org> wrote in message
news:<4085748f\$0\$16471\$61fed72c@news.rcn.com>...
> > Michal Kvasnicka wrote:
> >
> > > What is the most effective way to adaptive estimate freqs and phases
of the
> > > mixture (superposition) of the signals:
> > >
> > > s_i(t) = cos(2*pi*f_i*t+p_i)+n_i(t) ,
> > >
> > > where i=1,2, ..., N and n_i is additive gaussian noise.
> > >
> > > Michal
> >
> > Homework?
>
> Probably not. Frequency estimation is one of the more difficult
> practical analysis problems to work with. I have written a number
> of posts about various flavours of MUSIC, and a couple of other
> methods for frequency estimation. Once one starts to bring
> in amplitude and phase estimates as well, things become very difficult.
>
> Michal, for frequency estimation you should look at MUSIC and the
> Tufts/Kumaresan Forward-Backward Linear Prediction method. These
> techniques are designed for the "sum-of-sine" signals and some
> (but not all) are restricted to regularly sampled data. You should
> also take some time to read up on the Cramer-Raou Lower bound of
> variance of parameter estimates. The problem is that there are
> limits to how precise estimates of frequency and phase can be.
>
> Rune

```
```Hi Michal.

Michal> Thanks. But the MUSIC like methods estimate only
Michal> frequency. What about simultaneous estimation of the frequency
Michal> and phase? Do you know any suitable method and combination of
Michal> methods for this type of problem?

Michal> I know very well that C-R bound limitate the precision of the
Michal> final freq and phase estimation. But now I am looking for any
Michal> suitable method for simulataneous freq+phase estimation.

Given the frequencies, phases and amplitudes can be estimated using
least-squares. I suggest that you look into Petre Stoica's many
publications on nonlinear least-squares frequency estimation and
approximations of it.

http://www.syscon.uu.se/Personnel/ps/ref.html

--
```
```Hi Michal.

Michal> Thanks. But the MUSIC like methods estimate only
Michal> frequency. What about simultaneous estimation of the frequency
Michal> and phase? Do you know any suitable method and combination of
Michal> methods for this type of problem?

Michal> I know very well that C-R bound limitate the precision of the
Michal> final freq and phase estimation. But now I am looking for any
Michal> suitable method for simulataneous freq+phase estimation.

Couldn't help my self, so I started looking around. Have a look at
P. Stoica, H. Li, and J. Li, "Amplitude Estimation of Sinusoidal
Signals: Survey, New Results, and an Application", IEEE Trans. on
Signal Processing, vol. 48(2), Feb, 2000.

--
```
```Michal Kvasnicka wrote:

> No!!!!
...