imrep2ss

state-space realization of an impulse response

Calling Sequence

[sl]=imrep2ss(v [,deg])

Arguments

:v vector coefficients of impulse response, v(:,k) is the kth sample : :deg integer (order required) : :sl syslin list :

Description

Impulse response to linear system conversion (one input). v must have an even number of columns.

Examples

s=`poly`_(0,'s');
H=[1/(s+0.5);2/(s-0.4)]   //strictly proper
np=20;w=`ldiv`_(H('num'),H('den'),np);
rep=[w(1:np)';w(np+1:2*np)'];   //The impulse response
H1=`ss2tf`_(imrep2ss(rep))
z=`poly`_(0,'z');
H=(2*z^2-3.4*z+1.5)/(z^2-1.6*z+0.8)     //Proper transfer function
u=`zeros`_(1,20);u(1)=1;
rep=`rtitr`_(H('num'),H('den'),u);   //Impulse rep.
//   <=> rep=ldiv(H('num'),H('den'),20)
w=z*imrep2ss(rep)   //Realization with shifted impulse response
// i.e strictly proper to proper
H2=`ss2tf`_(w);

See Also

• frep2tf transfer function realization from frequency response
• arl2 SISO model realization by L2 transfer approximation
• time_id SISO least square identification
• armax armax identification
• markp2ss Markov parameters to state-space
• ldiv polynomial matrix long division