# [Eeglablist] EEG parameterization

Tim Mullen mullen.tim at gmail.com
Mon Jan 27 20:16:35 PST 2014

```PS: of course, X(t) and E(t) in my equations should be column vectors :)

On Mon, Jan 27, 2014 at 6:33 PM, Tim Mullen <mullen.tim at gmail.com> wrote:

> OK, there are two ways to do this.
>
> You can do it by hand, or you can do it automatically using SIFTs
> simulation package.
>
> For the former: you have write out the system matrix which contains the
> interaction coefficients at each lag.
>
> Let me demonstrate for a simple 2-dim VAR process of order 2:
>
> x1(t) = 0.95√2x1(t − 1) − 0.9025x1(t − 2) + e1(t)
> x2(t) = 0.5x1(t − 2) + e2(t)
>
> The lag-1 AR coefficient matrix is:
>
> [image: Inline image 4]
>
> and the lag-2 AR coefficient matrix is:
> [image: Inline image 3]
>
> The linear equation describing this system is then:
>
> [image: Inline image 7]
> where
> [image: Inline image 8]
> and
> [image: Inline image 9]
>
> For more complex systems, you will want to generate the A matrices automatically.
> For this you can use the SIFT function sim_genVARModelFromEq().
>
> You can also simulate data from this system of equations other routines in
> the SIFT simulation package.
> See the example in */scripts/SimulationExample.m. *Or, for a GUI
> experience, try this: *EEG = pop_sim_varmodel()*
>
> Here is an example of how to generate the "A" (system) matrices:
>
> format short
> % First, we write out the system of equations as a cell array of strings:% Although, this is very similar to how it will appear in most papers, we% must follow a precise convention as described in the help doc for% sim_genVARModelFromEq(). Particularly, notice how we use {<arg>} % when we wish to provide an inline expression (e.g. {0.95*sqrt(2)}) for a% coefficient, rather than a numeric value. Also note the use of "+" to% separate all terms of the equations and the convention xi and ei to% denote the ith data and noise terms.
> expr = {...'x1(t) = {0.95*sqrt(2)}*x1(t-1) + -0.9025*x1(t-2) + e1(t)', ...'x2(t) = 0.5*x1(t-2) + e2(t)', ...'x3(t) = -0.4*x1(t-3) + e3(t)', ...'x4(t) = -0.5*x1(t-2) + {0.25*sqrt(2)}*x4(t-1) + {0.25*sqrt(2)}*x5(t-1) + e4(t)', ...'x5(t) = {-0.25*sqrt(2)}*x4(t-1) + {0.25*sqrt(2)}*x5(t-1) + e5(t)'};
> ModelOrder = 3;
> NumChans = 5;
> % parse the equation expression and generate the system matrix [A1 A2 ... Ap]
> A = sim_genVARModelFromEq(expr,ModelOrder)
>
> A =
>
>     '0.95*sqrt(2)'    [0]    [0]    [            0]    [           0]    [-0.9025]    [0]    [0]    [0]    [0]    [      0]    [0]    [0]    [0]    [0]
>     [           0]    [0]    [0]    [            0]    [           0]    [ 0.5000]    [0]    [0]    [0]    [0]    [      0]    [0]    [0]    [0]    [0]
>     [           0]    [0]    [0]    [            0]    [           0]    [      0]    [0]    [0]    [0]    [0]    [-0.4000]    [0]    [0]    [0]    [0]
>     [           0]    [0]    [0]    '0.25*sqrt(2)'     '0.25*sqrt(2)'    [-0.5000]    [0]    [0]    [0]    [0]    [      0]    [0]    [0]    [0]    [0]
>     [           0]    [0]    [0]    '-0.25*sqrt(2)'    '0.25*sqrt(2)'    [      0]    [0]    [0]    [0]    [0]    [      0]    [0]    [0]    [0]    [0]
>
> % evaluate the inline terms involving sqrt():
> A = [cellfun(@(x) eval(num2str(x)), Aproto)]
> % NOTE: we could also do the evaluation using this code:% A = sim_genTVARcoeffs('Aproto',A,'ModelOrder',ModelOrder,'Nl',1,'ndisc',0);% A = A{1};
>
> A =
>
>     1.3435         0         0         0         0   -0.9025         0         0         0         0         0         0         0         0         0
>          0         0         0         0         0    0.5000         0         0         0         0         0         0         0         0         0
>          0         0         0         0         0         0         0         0         0         0   -0.4000         0         0         0         0
>          0         0         0    0.3536    0.3536   -0.5000         0         0         0         0         0         0         0         0         0
>          0         0         0   -0.3536    0.3536         0         0         0         0         0         0         0         0         0         0
>
> % print the VAR coefficient matrices for each lagfor k=1:ModelOrder
>     fprintf('------------------------------------------------\n');
>     fprintf('A%d = \n',k); disp(A(:,(k-1)*NumChans+1:k*NumChans));end
>
>
> ------------------------------------------------
> A1 =
>     1.3435         0         0         0         0
>          0         0         0         0         0
>          0         0         0         0         0
>          0         0         0    0.3536    0.3536
>          0         0         0   -0.3536    0.3536
>
> ------------------------------------------------
> A2 =
>    -0.9025         0         0         0         0
>     0.5000         0         0         0         0
>          0         0         0         0         0
>    -0.5000         0         0         0         0
>          0         0         0         0         0
>
> ------------------------------------------------
> A3 =
>          0         0         0         0         0
>          0         0         0         0         0
>    -0.4000         0         0         0         0
>          0         0         0         0         0
>          0         0         0         0         0
>
>
> Published with MATLAB® 7.14
>
>
>
> Best,
>
> Tim
>
>
>
>
>
>
> On Mon, Jan 27, 2014 at 4:10 PM, Ibtissem KHOUAJA BENFRADJ <
> ibtissem.khouaja at live.fr> wrote:
>
>>
>> andhelp me to better understand the needs of my work.
>>
>>
>> I extrcted the matrix chains EEG from an (.edf) file,
>> I want to find the linear equation that characterizes the dynamics of
>> these signals as described in the article:
>>  "A MATLAB toolbox for Granger causal connectivity analysis",
>>
>> x1(t) = 0.95 √2x1(t − 1) − 0.9025x1(t − 2) + w1(t)
>> x2(t) = 0.5x1(t − 2) + w2(t)
>> x3(t) = −0.4x1(t − 3) + w3(t)
>> x4(t) = −0.5x1(t − 2) + 0.25√2x4(t − 1) + 0.25√2x5(t − 1)+w4(t)
>> x5(t) = −0.25√2x4(t − 1) + 0.25√2x5(t − 1) +w5(t)
>>
>> how these factors can be extracted?
>>
>>
>>
>> PhD in computer science
>> Speciality Signal Processing
>> Laboratory LTIM, University of Monastir, Tunisia
>> http://www.labtim.org/accueil.php
>> Laboratory LIGM, Univerisity of Paris-East, France
>> http://ligm.u-pem.fr/
>>
>>
>>
>>
>> ------------------------------
>> From: mullen.tim at gmail.com
>> Date: Wed, 15 Jan 2014 18:26:48 -0800
>> Subject: Re: [Eeglablist] EEG parameterization
>> To: ibtissem.khouaja at live.fr
>> CC: eeglablist at sccn.ucsd.edu
>>
>> The function (<sift-root>/est/est_fitMVAR_DEKF.m) is included in SIFT
>> 1.0-beta and later, which you can obtain from the EEGLAB plugin manager or
>> the SIFT website.
>>
>> Best,
>> Tim
>>
>>
>> On Wed, Jan 15, 2014 at 5:28 AM, Ibtissem KHOUAJA BENFRADJ <
>> ibtissem.khouaja at live.fr> wrote:
>>
>>
>> Thank you Tim,
>> I actually need the non linear filter to study the EEG signaland to
>> extract these features.
>>
>> I find the linear filte (est_fitMVARKalman) on the net but I can't find
>> the socond one (est_fitMVAREKF).
>> Can you send me the link.
>>
>> thanks a lot.
>> -----------
>> PhD in computer science
>> Speciality Signal Processing
>> Laboratory LTIM, University of Monastir, Tunisia
>> http://www.labtim.org/accueil.php
>> Laboratory LIGM, Univerisity of Paris-East, France
>> http://ligm.u-pem.fr/
>>
>>
>>
>>
>> > Date: Wed, 8 Jan 2014 18:04:46 -0800
>>
>> > Subject: Re: [Eeglablist] EEG parameterization
>> > From: mullen.tim at gmail.com
>> > To: ibtissem.khouaja at live.fr; eeglablist at sccn.ucsd.edu
>> > CC:
>> >
>> > There are linear and nonlinear kalman filter-based multivariate
>> autoregressive implementations in the Source Information Flow Toolbox for
>> EEGLAB. See est_fitMVARKalman and est_fitMVARDEKF.
>> >
>> > Tim
>> >
>> > -----Original Message-----
>> > Date: Wednesday, January 08, 2014 1:40:42 pm
>> > To: "EEGLAB-list" <eeglablist at sccn.ucsd.edu>
>> > From: "Ibtissem KHOUAJA BENFRADJ" <ibtissem.khouaja at live.fr>
>> > Subject: Re: [Eeglablist] EEG parameterization
>> >
>> >
>> >
>> >
>> >
>> > Thank you very much for your answers and happy new year 2014.
>> > On my first question, I am based on your set and literature and I will
>> present the EEG signal from a set of evolutionary parameters based on the
>> Kalman filter.
>> > This gives the possibility of reconstructing the signal and to predict
>> its evolution.
>> > Is there someone who work with this type of auto-regressive filter?I
>> need the algorithm in Matlab.
>> > Thank a lot for your precious help, Ibtissem
>> >
>> >
>> >
>> >
>> ---------------------------------------------------------------------------
>> >
>> ---------------------------------------------------------------------------
>> > > From: poil.simonshlomo at gmail.com
>> > > Date: Thu, 19 Dec 2013 21:43:51 +0100
>> > > Subject: Re: [Eeglablist] EEG parameterization
>> > > To: ibtissem.khouaja at live.fr
>> > > CC: eeglablist at sccn.ucsd.edu
>> > >
>> > > Dear Ibtissem,
>> > >
>> > > There are several ways you can characterize an EEG signal. The two
>> > > basic are frequency and amplitude in different frequency bands (and
>> > > spatial location). You can see more here:
>> >
>>
>>
>>
>>
>> --
>> ---------  αντίληψη -----------
>>
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>
>
>
> --
> ---------  αντίληψη -----------
>

--
---------  αντίληψη -----------
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```