arma

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")