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From: rshahriar on 8 Jul 2010 15:54 I have sum of damped sinusoidal signal (to be precise, sum of 4 damped sine wave) corrupted by noise. I goal is to extract the poles (as well as damping factor and frequency). Signal Looks like: y(t) = x(t) + n(t) = SUM_{i}{ R_{i} exp(s_{i}t)} + n(t) where R is Residue or complex amplitude and s = a + b*i, a = damping factor and b = 2*pi*f. I am interested to use Yule Walker AR Estimation process to find s. I know that using MATLAB “aryule” I could find out the AR parameters. Now I am confused about next steps. Can i directly fins out s from AR coefficients found by aryule? or I have to do something more? How can I find the poles ( s = a + j*b), here? Using SVD or any other method?
From: Rune Allnor on 8 Jul 2010 16:07 On 8 Jul, 21:54, "rshahriar" <cshahria(a)n_o_s_p_a_m.vt.edu> wrote: > I have sum of damped sinusoidal signal (to be precise, sum of 4 damped sine > wave) corrupted by noise. I goal is to extract the poles (as well as > damping factor and frequency). > > Signal Looks like: > > y(t) = x(t) + n(t) = SUM_{i}{ R_{i} exp(s_{i}t)} + n(t) > > where R is Residue or complex amplitude and s = a + b*i, a = damping factor > and b = 2*pi*f. > > I am interested to use Yule Walker AR Estimation process to find s. > > I know that using MATLAB aryule I could find out the AR parameters. > > Now I am confused about next steps. Can i directly fins out s from AR > coefficients found by aryule? or I have to do something more? > > How can I find the poles ( s = a + j*b), here? Using SVD or any other > method? Read up on the basics. There will be a number of reperesentations of the AR coefficients. You will need to sort oot 1) The various representations of the AR coefficients and the relations between them 2) The various representations of your model and their relations with the AR coefficient representations you found under step 1. Hint: *One* representation of the AR coefficients will map 1:1 with *one* representation of your signal *model*. Which means that the numbers that pop out at the end will only make sense if your signal actually complies to the assumed model. Rune
From: rshahriar on 9 Jul 2010 11:25 >On 8 Jul, 21:54, "rshahriar" <cshahria(a)n_o_s_p_a_m.vt.edu> wrote: >> I have sum of damped sinusoidal signal (to be precise, sum of 4 damped si= >ne >> wave) corrupted by noise. I goal is to extract the poles (as well as >> damping factor and frequency). >> >> Signal Looks like: >> >> y(t) =3D x(t) + n(t) =3D SUM_{i}{ R_{i} exp(s_{i}t)} + n(t) >> >> where R is Residue or complex amplitude and s =3D a + b*i, a =3D damping = >factor >> and b =3D 2*pi*f. >> >> I am interested to use Yule Walker AR Estimation process to find s. >> >> I know that using MATLAB =93aryule=94 I could find out the AR parameters. >> >> Now I am confused about next steps. Can i directly fins out s from AR >> coefficients found by aryule? or I have to do something more? >> >> How can I find the poles ( s =3D a + j*b), here? Using SVD or any other >> method? > >Read up on the basics. There will be a number of reperesentations >of the AR coefficients. You will need to sort oot > >1) The various representations of the AR coefficients and the > relations between them > >2) The various representations of your model and their relations > with the AR coefficient representations you found under step 1. > >Hint: *One* representation of the AR coefficients will map 1:1 >with *one* representation of your signal *model*. Which means >that the numbers that pop out at the end will only make sense >if your signal actually complies to the assumed model. > >Rune > Thanks for the hint. but i have to admit that i am a bit confused here. AR coefficients are all what i have. need to extract the pole from there.
From: Rune Allnor on 9 Jul 2010 12:49 On 9 Jul, 17:25, "rshahriar" <cshahria(a)n_o_s_p_a_m.vt.edu> wrote: > >On 8 Jul, 21:54, "rshahriar" <cshahria(a)n_o_s_p_a_m.vt.edu> wrote: > >> I have sum of damped sinusoidal signal (to be precise, sum of 4 damped > si= > >ne > >> wave) corrupted by noise. I goal is to extract the poles (as well as > >> damping factor and frequency). > > >> Signal Looks like: > > >> y(t) =3D x(t) + n(t) =3D SUM_{i}{ R_{i} exp(s_{i}t)} + n(t) > > >> where R is Residue or complex amplitude and s =3D a + b*i, a =3D damping > = > >factor > >> and b =3D 2*pi*f. > > >> I am interested to use Yule Walker AR Estimation process to find s. > > >> I know that using MATLAB =93aryule=94 I could find out the AR > parameters. > > >> Now I am confused about next steps. Can i directly fins out s from AR > >> coefficients found by aryule? or I have to do something more? > > >> How can I find the poles ( s =3D a + j*b), here? Using SVD or any other > >> method? > > >Read up on the basics. There will be a number of reperesentations > >of the AR coefficients. You will need to sort oot > > >1) The various representations of the AR coefficients and the > > relations between them > > >2) The various representations of your model and their relations > > with the AR coefficient representations you found under step 1. > > >Hint: *One* representation of the AR coefficients will map 1:1 > >with *one* representation of your signal *model*. Which means > >that the numbers that pop out at the end will only make sense > >if your signal actually complies to the assumed model. > > >Rune > > Thanks for the hint. but i have to admit that i am a bit confused here. AR > coefficients are all what i have. need to extract the pole from there. Then start with figuring out the relation between the poles and the AR coefficients. Read the textbook. Rune

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