arma Scilab arma library

## Description

Armax processes can be coded with Scilab tlist of type `'ar'`. `armac` is used to build `Armax` scilab object. An `'ar'` tlist contains the fields `['a','b','d','ny','nu','sig']`.

armac

  this function creates a Scilab tlist which code an Armax process `A(z^-1)y= B(z^-1)u + D(z^-1)sig*e(t)`

      -->ar=armac([1,2],[3,4],1,1,1,sig);

      -->ar('a')
       ans  =

      !   1.    2. !
      -->ar('sig')
       ans  =

          1.

armap(ar [,out])

  Display the armax equation associated with `ar`

armap_p(ar [,out])

  Display the armax equation associated with `ar` using polynomial matrix display.

[A,B,D]=armap2p(ar)

  extract polynomial matrices from ar representation

armax

  is used to identify the coefficients of a n-dimensional ARX process `A(z^-1)y= B(z^-1)u + sig*e(t)`

armax1

  armax1 is used to identify the coefficients of a 1-dimensional ARX process `A(z^-1)y= B(z^-1)u + D(z^-1)sig*e(t)`

arsimul

  armax trajectory simulation.

narsimul

  armax simulation ( using rtitr)

odedi

  Simple tests of ode and arsimul. Tests the option 'discret' of ode

prbs_a

  pseudo random binary sequences generation

reglin

  Linear regression

## Example

    // Example extracted from the demo arma3.dem.sce in the cacsd module
    // Spectral power estimation
    // ( form Sawaragi et all)
    m = 18;
    a = [1,-1.3136,1.4401,-1.0919,+0.83527];
    b = [0.0,0.13137,0.023543,0.10775,0.03516];
    u = rand(1,1000,'n');
    z = arsimul(a,b,[0],0,u);

    //----Using macro mese
    [sm,fr]=mese(z,m);

    //----The theoretical result

    function gx=gxx(z,a,b)
      w  = exp(-%i*2*%pi*z*(0:4))'
      gx = abs(b*w)^2/(abs(a*w)^2);
    endfunction

    res=[];
    for x=fr
      res=[ res, gxx(x,a,b)];
    end

    //----using armax estimation of order  (4,4)
    // it's a bit tricky because we are not supposed to know the order

    [arc,la,lb,sig,resid]=armax(4,4,z,u);
    res1=[];
    for x=fr
      res1=[ res1, gxx(x,la(1),lb(1))];
    end

    //-- visualization of the results
    plot2d([fr;fr;fr]',[20*log10(sm/sm(1));20*log10(res/res(1));20*log10(res1/res1(1))]',[2,1,-1])
    legend(["Using macro mese";"Theoretical value";"Arma identification"])
    xtitle("Spectral power","frequency","spectral estimate")

m = 18; a = [1,-1.3136,1.4401,-1.0919,+0.83527]; b = [0.0,0.13137,0.023543,0.10775,0.03516]; u = rand(1,1000,'n'); z = arsimul(a,b,[0],0,u); [sm,fr]=mese(z,m); function gx=gxx(z,a,b) w = exp(-%i*2*%pi*z*(0:4))' gx = abs(b*w)^2/(abs(a*w)^2); endfunction res=[]; for x=fr res=[ res, gxx(x,a,b)]; end [arc,la,lb,sig,resid]=armax(4,4,z,u); res1=[]; for x=fr res1=[ res1, gxx(x,la(1),lb(1))]; end plot2d([fr;fr;fr]',[20*log10(sm/sm(1));20*log10(res/res(1));20*log10(res1/res1(1))]',[2,1,-1]) legend(["Using macro mese";"Theoretical value";"Arma identification"]) xtitle("Spectral power","frequency","spectral estimate")