Please note that the recommended version of Scilab is 6.1.1. This page might be outdated.
See the recommended documentation of this function
dimension of the observation
desired dimension of the state vector for the approximated model
- H, F, G
relevant matrices of the Markovian model
Function which computes the matrices
H, F, G of a Markovian
representation by the principal hankel
component approximation method, from the hankel matrix built
from the covariance sequence of a stochastic process.
//This example may usefully be compared with the results from //the 'levin' macro (see the corresponding help and example) // //We consider the process defined by two sinusoids (1Hz and 2 Hz) //in additive Gaussian noise (this is the observation); //the simulated process is sampled at 10 Hz. t=0:.1:100;rand('normal'); y=sin(2*%pi*t)+sin(2*%pi*2*t);y=y+rand(y);plot(t,y) //covariance of y nlag=128; c=corr(y,nlag); //hankel matrix from the covariance sequence //(we can choose to take more information from covariance //by taking greater n and m; try it to compare the results ! n=20;m=20; h=hank(n,m,c); //compute the Markov representation (mh,mf,mg) //We just take here a state dimension equal to 4 : //this is the rather difficult problem of estimating the order ! //Try varying ns ! //(the observation dimension is here equal to one) ns=4; [mh,mf,mg]=phc(h,1,ns); //verify that the spectrum of mf contains the //frequency spectrum of the observed process y //(remember that y is sampled -in our example //at 10Hz (T=0.1s) so that we need //to retrieve the original frequencies through the log //and correct scaling by the frequency sampling) s=spec(mf);s=log(s); s=s/2/%pi/.1; //now we get the estimated spectrum imag(s),
- levin — Toeplitz system solver by Levinson algorithm (multidimensional)
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