Reply by Andor March 7, 20072007-03-07
On 7 Mrz., 15:38, "gauthief" <frederic.gauth...@orange-ftgroup.com>
wrote:
> On 7 mar, 12:14, "Andor" <andor.bari...@gmail.com> wrote: > > > > > > > On 7 Mrz., 10:56, "gauthief" <frederic.gauth...@orange-ftgroup.com> > > wrote: > > > > On 7 mar, 09:23, "Andor" <andor.bari...@gmail.com> wrote: > > > > > 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 se=
nt 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 frequen=
cy
> > > > > 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) =3D cos(w0 t) > > > > > into the system. The output will be of the form > > > > > y(t) =3D a cos(w0 t + phi). > > > > > The frequency response is > > > > > H(w) =3D 1 + A exp(- j w T). > > > > > You can measure the two values a and phi and get two equations > > > > > |H(w0)| =3D a, > > > > arg(H(w0)) =3D phi, > > > > > from which you can determine A and T modulo w0/(2 pi). This means t=
hat
> > > > if your delay is large, you need very low frequency measurement ton=
e=2E
> > > > > Regards, > > > > Andor- Masquer le texte des messages pr=E9c=E9dents - > > > > > - Afficher le texte des messages pr=E9c=E9dents - > > > > andor > > > in fact for each transmited frequency x(t)=3D a cos(w0t) the recived > > > signal is y(t)=3Da1cos(w0(t-T1))+a2cos(w0(t-T2)+....+ak(cos(w0(t-Tk)) > > > If there are K reflections I would think you need K input / output > > measurements (each at different frequency) to determine the > > parameters. You then have 2 K non-linear equations for the 2 K > > unkowns, and you should theoretically be able to solve that: > > > |H(w_k)| =3D a_k > > arg( H(w_k) ) =3D phi_k, > > > 0 <=3D k <=3D K-1. You must know K in advance. > > > Regards, > > Andor > > > > K is the number of paths and ak et cos are complex > > > ak is the amplitude of the k-th reflection, right? > > Andor > > yes ak is the amplitude of the k-th reflection. > > I know the number of reflection by computing the Singular values of > the autocorrelation function and i keep the highest value. The number > of singular values is, I think, the number of paths
So, then you only have to solve that system of non-linear equations. You must however make sure that the periods of your measurement tones are larger than the highest occuring delay. Regards, Andor
Reply by gauthief March 7, 20072007-03-07
On 7 mar, 12:14, "Andor" <andor.bari...@gmail.com> wrote:
> On 7 Mrz., 10:56, "gauthief" <frederic.gauth...@orange-ftgroup.com> > wrote: > > > > > > > On 7 mar, 09:23, "Andor" <andor.bari...@gmail.com> wrote: > > > > 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 s=
hift
> > > > > > 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) =3D cos(w0 t) > > > > into the system. The output will be of the form > > > > y(t) =3D a cos(w0 t + phi). > > > > The frequency response is > > > > H(w) =3D 1 + A exp(- j w T). > > > > You can measure the two values a and phi and get two equations > > > > |H(w0)| =3D a, > > > arg(H(w0)) =3D 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- Masquer le texte des messages pr=E9c=E9dents - > > > > - Afficher le texte des messages pr=E9c=E9dents - > > > andor > > in fact for each transmited frequency x(t)=3D a cos(w0t) the recived > > signal is y(t)=3Da1cos(w0(t-T1))+a2cos(w0(t-T2)+....+ak(cos(w0(t-Tk)) > > If there are K reflections I would think you need K input / output > measurements (each at different frequency) to determine the > parameters. You then have 2 K non-linear equations for the 2 K > unkowns, and you should theoretically be able to solve that: > > |H(w_k)| =3D a_k > arg( H(w_k) ) =3D phi_k, > > 0 <=3D k <=3D K-1. You must know K in advance. > > Regards, > Andor > > > K is the number of paths and ak et cos are complex > > ak is the amplitude of the k-th reflection, right? > > Regards, > Andor- Masquer le texte des messages pr=E9c=E9dents - > > - Afficher le texte des messages pr=E9c=E9dents -
Andor yes ak is the amplitude of the k-th reflection. I know the number of reflection by computing the Singular values of the autocorrelation function and i keep the highest value. The number of singular values is, I think, the number of paths
Reply by Rune Allnor March 7, 20072007-03-07
On 7 Mar, 12:50, "Andor" <andor.bari...@gmail.com> wrote:
> On 7 Mrz., 12:26, "Rune Allnor" <all...@tele.ntnu.no> wrote:
> > That's a different problem than the OP outlined. > > Well I specifically asked him if that was the model, and he said yes.
> It is very well possible to determine the system parameters using 2 K > (or 2 (K+1)) measurements of sinusoidal input /output pairs. No magic > required.
Provided you actually *have* the input-output pair. If you don't, you are stuck. Rune
Reply by Andor March 7, 20072007-03-07
On 7 Mrz., 12:26, "Rune Allnor" <all...@tele.ntnu.no> wrote:
> On 7 Mar, 11:59, "Andor" <andor.bari...@gmail.com> wrote: > > > > > > > On 7 Mrz., 10:54, "Rune Allnor" <all...@tele.ntnu.no> wrote: > > > > On 7 Mar, 09:29, "Andor" <andor.bari...@gmail.com> wrote: > > > > > 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. > > > > There is a phase taht is messed up, but that's it. > > > > > > = C/2(exp(jwt)+exp(-jwt)) > > > > > = C cos(wt). > > > > > You don't *really* believe that, do you :-). > > > > For the pedants: > > > > = C/2(exp(jwt+theta)+exp(-jwt+theta)) > > > You're getting closer :-). > > > > = C cos(wt + theta) > > > > for some phase angle theta which is left for the > > > reader to find. OK? > > > > Now, this doesn't change the basic conclusion: > > > That it is impossible to use a time-domain measurement > > > to find the coefficients of a sum of two sines at the > > > same frequency. > > > If the channel model is 1 + A z^-T, with unknown A and T, then it is > > possible to determine A and T from just the measurement of input and > > output sinusoid. I outlined the procedure in another post. > > That's a different problem than the OP outlined.
Well I specifically asked him if that was the model, and he said yes. It turns out that his channel model was slightly more complex, including K rather than one reflection. This is a rather simple system identification problem, with a K-th order FIR model. It is very well possible to determine the system parameters using 2 K (or 2 (K+1)) measurements of sinusoidal input /output pairs. No magic required. Regards, Andor
Reply by Rune Allnor March 7, 20072007-03-07
On 7 Mar, 11:59, "Andor" <andor.bari...@gmail.com> wrote:
> On 7 Mrz., 10:54, "Rune Allnor" <all...@tele.ntnu.no> wrote: > > > > > > > On 7 Mar, 09:29, "Andor" <andor.bari...@gmail.com> wrote: > > > > 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. > > > There is a phase taht is messed up, but that's it. > > > > > = C/2(exp(jwt)+exp(-jwt)) > > > > = C cos(wt). > > > > You don't *really* believe that, do you :-). > > > For the pedants: > > > = C/2(exp(jwt+theta)+exp(-jwt+theta)) > > You're getting closer :-). > > > = C cos(wt + theta) > > > for some phase angle theta which is left for the > > reader to find. OK? > > > Now, this doesn't change the basic conclusion: > > That it is impossible to use a time-domain measurement > > to find the coefficients of a sum of two sines at the > > same frequency. > > If the channel model is 1 + A z^-T, with unknown A and T, then it is > possible to determine A and T from just the measurement of input and > output sinusoid. I outlined the procedure in another post.
That's a different problem than the OP outlined. Your approach requires the analyst to control the source. The OP has -- or at least gives the impression -- one measurement in a running system, there is nothing in his posts to suggest that he controls the source. It's the easiest thing in the world to come up with data analysis solutions when you break the boundary conditions of the experiment. Staying inside the constraints makes it a whole different game. Rune
Reply by Andor March 7, 20072007-03-07
On 7 Mrz., 10:56, "gauthief" <frederic.gauth...@orange-ftgroup.com>
wrote:
> On 7 mar, 09:23, "Andor" <andor.bari...@gmail.com> wrote: > > > > > > > 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 shi=
ft
> > > > > 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 i=
nto
> > > > 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) =3D cos(w0 t) > > > into the system. The output will be of the form > > > y(t) =3D a cos(w0 t + phi). > > > The frequency response is > > > H(w) =3D 1 + A exp(- j w T). > > > You can measure the two values a and phi and get two equations > > > |H(w0)| =3D a, > > arg(H(w0)) =3D 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- Masquer le texte des messages pr=E9c=E9dents - > > > - Afficher le texte des messages pr=E9c=E9dents - > > andor > in fact for each transmited frequency x(t)=3D a cos(w0t) the recived > signal is y(t)=3Da1cos(w0(t-T1))+a2cos(w0(t-T2)+....+ak(cos(w0(t-Tk))
If there are K reflections I would think you need K input / output measurements (each at different frequency) to determine the parameters. You then have 2 K non-linear equations for the 2 K unkowns, and you should theoretically be able to solve that: |H(w_k)| =3D a_k arg( H(w_k) ) =3D phi_k, 0 <=3D k <=3D K-1. You must know K in advance. Regards, Andor
> K is the number of paths and ak et cos are complex
ak is the amplitude of the k-th reflection, right? Regards, Andor
Reply by Andor March 7, 20072007-03-07
On 7 Mrz., 10:54, "Rune Allnor" <all...@tele.ntnu.no> wrote:
> On 7 Mar, 09:29, "Andor" <andor.bari...@gmail.com> wrote: > > > > > > > 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. > > There is a phase taht is messed up, but that's it. > > > > = C/2(exp(jwt)+exp(-jwt)) > > > = C cos(wt). > > > You don't *really* believe that, do you :-). > > For the pedants: > > = C/2(exp(jwt+theta)+exp(-jwt+theta))
You're getting closer :-).
> = C cos(wt + theta) > > for some phase angle theta which is left for the > reader to find. OK? > > Now, this doesn't change the basic conclusion: > That it is impossible to use a time-domain measurement > to find the coefficients of a sum of two sines at the > same frequency.
If the channel model is 1 + A z^-T, with unknown A and T, then it is possible to determine A and T from just the measurement of input and output sinusoid. I outlined the procedure in another post. Regards, Andor
Reply by gauthief March 7, 20072007-03-07
On 7 mar, 09:23, "Andor" <andor.bari...@gmail.com> wrote:
> 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) =3D cos(w0 t) > > into the system. The output will be of the form > > y(t) =3D a cos(w0 t + phi). > > The frequency response is > > H(w) =3D 1 + A exp(- j w T). > > You can measure the two values a and phi and get two equations > > |H(w0)| =3D a, > arg(H(w0)) =3D 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- Masquer le texte des messages pr=E9c=E9dents - > > - Afficher le texte des messages pr=E9c=E9dents -
andor in fact for each transmited frequency x(t)=3D a cos(w0t) the recived signal is y(t)=3Da1cos(w0(t-T1))+a2cos(w0(t-T2)+....+ak(cos(w0(t-Tk)) K is the number of paths and ak et cos are complex
Reply by Rune Allnor March 7, 20072007-03-07
On 7 Mar, 09:29, "Andor" <andor.bari...@gmail.com> wrote:
> 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.
There is a phase taht is messed up, but that's it.
> > = C/2(exp(jwt)+exp(-jwt)) > > = C cos(wt). > > You don't *really* believe that, do you :-).
For the pedants: = C/2(exp(jwt+theta)+exp(-jwt+theta)) = C cos(wt + theta) for some phase angle theta which is left for the reader to find. OK? Now, this doesn't change the basic conclusion: That it is impossible to use a time-domain measurement to find the coefficients of a sum of two sines at the same frequency. Try with MUSIC, try with ICA, try black magic: The above is a trivial, fundamental property of the model which no algorithm in the world can change. Rune
Reply by gauthief March 7, 20072007-03-07
On 7 mar, 04:13, "PARTICLEREDDY (STRAYDOG)" <particlere...@gmail.com>
wrote:
> 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- Masquer le texte des messages pr=E9c=E9d=
ents -
> > - Afficher le texte des messages pr=E9c=E9dents -
particleraddy, i will look the ICA method thank you for your answer