MUSIC in time domain

Started by March 6, 2007
```hi evry body

i have seen a lot of mail about MUSIC to determine AOA but I would
like to separate signals at one frequency separated by a pase shift
due to propagation. does any body have a soft to do that?

thank you

Frederic

```
```Frederic wrote:
> ... I would
> like to separate signals at one frequency separated by a pase shift
> due to propagation. does any body have a soft to do that?

So you have a signal at one frequency, say w0. The signal is sent into
a channel with transfer function

1 + A z^-T,

where A is the weighting and T is the delay of the echo. Using an
input/output sinusoid pair at w0, you want to determine A and T. Is
that correct?

Regards,
Andor

```
```On 6 mar, 15:18, "Andor" <andor.bari...@gmail.com> wrote:
> Frederic wrote:
> > ... I would
> > like to separate signals at one frequency separated by a pase shift
> > due to propagation. does any body have a soft to do that?
>
> So you have a signal at one frequency, say w0. The signal is sent into
> a channel with transfer function
>
> 1 + A z^-T,
>
> where A is the weighting and T is the delay of the echo. Using an
> input/output sinusoid pair at w0, you want to determine A and T. Is
> that correct?
>
> Regards,
> Andor

yes thats correct, in fact I have the signal at different frequency
values but i have use an algorithm (Generalise Pencil of Function) to
obtaine the signal for each frequency. The basic signal is the
transfert function of the electrical line in an house where there is a
lot of reflection and i would like, if possible, to obtaine the
informations for each path.
thank you

Regards

Fr=E9d=E9ric

```
```On 6 Mar, 16:03, "gauthief" <frederic.gauth...@orange-ftgroup.com>
wrote:
> On 6 mar, 15:18, "Andor" <andor.bari...@gmail.com> wrote:
>
>
>
>
>
> > Frederic wrote:
> > > ... I would
> > > like to separate signals at one frequency separated by a pase shift
> > > due to propagation. does any body have a soft to do that?
>
> > So you have a signal at one frequency, say w0. The signal is sent into
> > a channel with transfer function
>
> > 1 + A z^-T,
>
> > where A is the weighting and T is the delay of the echo. Using an
> > input/output sinusoid pair at w0, you want to determine A and T. Is
> > that correct?
>
> > Regards,
> > Andor
>
> yes thats correct, in fact I have the signal at different frequency
> values but i have use an algorithm (Generalise Pencil of Function) to
> obtaine the signal for each frequency. The basic signal is the
> transfert function of the electrical line in an house where there is a
> lot of reflection and i would like, if possible, to obtaine the
> informations for each path.

So you want to find the parameters of a model

f(t) = A cos(wt) + B cos(wt+phi)

Let's take a closer look:

f(t) = A/2 (exp(jwt)+exp(-jwt)) + B/2 (exp(jwt+phi)+exp(-jwt-phi))
= (A+B)exp(phi)/2 (exp(jwt) + exp(-jwt))
= C/2(exp(jwt)+exp(-jwt))
= C cos(wt).

So using a time domain measuremet, you can not separate
the signal from the reflection.

Rune

```
```On 6 mar, 16:55, "Rune Allnor" <all...@tele.ntnu.no> wrote:
> On 6 Mar, 16:03, "gauthief" <frederic.gauth...@orange-ftgroup.com>
> wrote:
>
>
>
>
>
> > On 6 mar, 15:18, "Andor" <andor.bari...@gmail.com> wrote:
>
> > > Frederic wrote:
> > > > ... I would
> > > > like to separate signals at one frequency separated by a pase shift
> > > > due to propagation. does any body have a soft to do that?
>
> > > So you have a signal at one frequency, say w0. The signal is sent into
> > > a channel with transfer function
>
> > > 1 + A z^-T,
>
> > > where A is the weighting and T is the delay of the echo. Using an
> > > input/output sinusoid pair at w0, you want to determine A and T. Is
> > > that correct?
>
> > > Regards,
> > > Andor
>
> > yes thats correct, in fact I have the signal at different frequency
> > values but i have use an algorithm (Generalise Pencil of Function) to
> > obtaine the signal for each frequency. The basic signal is the
> > transfert function of the electrical line in an house where there is a
> > lot of reflection and i would like, if possible, to obtaine the
> > informations for each path.
>
> So you want to find the parameters of a model
>
> f(t) =3D A cos(wt) + B cos(wt+phi)
>
> Let's take a closer look:
>
> f(t) =3D A/2 (exp(jwt)+exp(-jwt)) + B/2 (exp(jwt+phi)+exp(-jwt-phi))
>      =3D (A+B)exp(phi)/2 (exp(jwt) + exp(-jwt))
>      =3D C/2(exp(jwt)+exp(-jwt))
>      =3D C cos(wt).
>
> So using a time domain measuremet, you can not separate
> the signal from the reflection.
>
> Rune- Masquer le texte des messages pr=E9c=E9dents -
>
> - Afficher le texte des messages pr=E9c=E9dents -

ok, thank you
y have tryed but with non succ=E8s the obtained result give the delay
corresponding to the number of samples used to construct the
autocorrelation function, so i thought that my programmation was
wrong.

Regards

Fr=E9d=E9ric

```
```On Mar 6, 1:21 am, "gauthief" <frederic.gauth...@orange-ftgroup.com>
wrote:
> hi evry body
>
> i have seen a lot of mail about MUSIC to determine AOA but I would
> like to separate signals at one frequency separated by a pase shift
> due to propagation. does any body have a soft to do that?

Is the source frequency a pure unmodulated sinusoid, or is it,
or can it be, modulated in any way?  Is the phase shifted portion
of the signal combined purely linearly, or are the any non-linear
effects between the signals?

Even your AC line might be modulated, by, for instance, your
neighbor's well pump relay kicking in, if you are on the same
transformer.

IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

```
```hi,
I believe..this can be done in ICA

http://www.cs.helsinki.fi/u/ahyvarin/whatisica.shtml

i remember..once..one of my colleague..was attempting using ICA..do
look at it once..

may be the seperation could be easy..but ..trying out different
methods..get a chance to know others..thats the good thing i guess

particlereddy

On Mar 6, 11:51 pm, "Ron N." <rhnlo...@yahoo.com> wrote:
> On Mar 6, 1:21 am, "gauthief" <frederic.gauth...@orange-ftgroup.com>
> wrote:
>
> > hi evry body
>
> > i have seen a lot of mail about MUSIC to determine AOA but I would
> > like to separate signals at one frequency separated by a pase shift

> > due to propagation. does any body have a soft to do that?
>
> Is the source frequency a pure unmodulated sinusoid, or is it,
> or can it be, modulated in any way?  Is the phase shifted portion
> of the signal combined purely linearly, or are the any non-linear
> effects between the signals?
>
> Even your AC line might be modulated, by, for instance, your
> neighbor's well pump relay kicking in, if you are on the same
> transformer.
>
> IMHO. YMMV.
> --
> rhn A.T nicholson d.0.t C-o-M

```
```On 6 Mrz., 16:03, "gauthief" <frederic.gauth...@orange-ftgroup.com>
wrote:
> On 6 mar, 15:18, "Andor" <andor.bari...@gmail.com> wrote:
>
>
>
>
>
> > Frederic wrote:
> > > ... I would
> > > like to separate signals at one frequency separated by a pase shift
> > > due to propagation. does any body have a soft to do that?
>
> > So you have a signal at one frequency, say w0. The signal is sent into
> > a channel with transfer function
>
> > 1 + A z^-T,
>
> > where A is the weighting and T is the delay of the echo. Using an
> > input/output sinusoid pair at w0, you want to determine A and T. Is
> > that correct?
>
> > Regards,
> > Andor
>
> yes thats correct, in fact I have the signal at different frequency
> values but i have use an algorithm (Generalise Pencil of Function) to
> obtaine the signal for each frequency.

I wish I knew what the (Generalise Pencil of Function) algorithm is.
Until then, you can procesd as follows:

Input the signal

x(t) = cos(w0 t)

into the system. The output will be of the form

y(t) = a cos(w0 t + phi).

The frequency response is

H(w) = 1 + A exp(- j w T).

You can measure the two values a and phi and get two equations

|H(w0)| = a,
arg(H(w0)) = phi,

from which you can determine A and T modulo w0/(2 pi). This means that
if your delay is large, you need very low frequency measurement tone.

Regards,
Andor

```
```On 6 Mrz., 16:55, "Rune Allnor" <all...@tele.ntnu.no> wrote:
> On 6 Mar, 16:03, "gauthief" <frederic.gauth...@orange-ftgroup.com>
> wrote:
>
>
>
>
>
> > On 6 mar, 15:18, "Andor" <andor.bari...@gmail.com> wrote:
>
> > > Frederic wrote:
> > > > ... I would
> > > > like to separate signals at one frequency separated by a pase shift
> > > > due to propagation. does any body have a soft to do that?
>
> > > So you have a signal at one frequency, say w0. The signal is sent into
> > > a channel with transfer function
>
> > > 1 + A z^-T,
>
> > > where A is the weighting and T is the delay of the echo. Using an
> > > input/output sinusoid pair at w0, you want to determine A and T. Is
> > > that correct?
>
> > > Regards,
> > > Andor
>
> > yes thats correct, in fact I have the signal at different frequency
> > values but i have use an algorithm (Generalise Pencil of Function) to
> > obtaine the signal for each frequency. The basic signal is the
> > transfert function of the electrical line in an house where there is a
> > lot of reflection and i would like, if possible, to obtaine the
> > informations for each path.
>
> So you want to find the parameters of a model
>
> f(t) = A cos(wt) + B cos(wt+phi)
>
> Let's take a closer look:
>
> f(t) = A/2 (exp(jwt)+exp(-jwt)) + B/2 (exp(jwt+phi)+exp(-jwt-phi))
>      = (A+B)exp(phi)/2 (exp(jwt) + exp(-jwt))

I would rethink the above two lines.

>      = C/2(exp(jwt)+exp(-jwt))
>      = C cos(wt).

You don't *really* believe that, do you :-).

>
> So using a time domain measuremet, you can not separate
> the signal from the reflection.
>
> Rune

Regards,
Andor

```
```On 6 mar, 19:51, "Ron N." <rhnlo...@yahoo.com> wrote:
> On Mar 6, 1:21 am, "gauthief" <frederic.gauth...@orange-ftgroup.com>
> wrote:
>
> > hi evry body
>
> > i have seen a lot of mail about MUSIC to determine AOA but I would
> > like to separate signals at one frequency separated by a pase shift
> > due to propagation. does any body have a soft to do that?
>
> Is the source frequency a pure unmodulated sinusoid, or is it,
> or can it be, modulated in any way?  Is the phase shifted portion
> of the signal combined purely linearly, or are the any non-linear
> effects between the signals?
>
> Even your AC line might be modulated, by, for instance, your
> neighbor's well pump relay kicking in, if you are on the same
> transformer.
>
> IMHO. YMMV.
> --
> rhn A.T nicholson d.0.t C-o-M

good morning

the source is frequency is not modulated and it should be a lot work
to perform a modulation. I am now try to synchronize the transmission
and the reiciver using a radio link, so if I can keep in memorie the
phase of the transmitted signal i can do a king of radar.

I have to program to see the phase shift. what is the idea?