Hello, I have a transfer function from ARMA or AR model having some high order. I want to obtain H(s). My approach is to assume that H(s) will have a form that will result in a high H(z) ARMA/AR model , and find a relation between these two!! I would appertiate any suggestion or comment,

# From Z-transform to Laplace

Started by ●June 17, 2009

Reply by ●June 17, 20092009-06-17

On 17 Jun, 12:28, "m.alawieh" <m.alaw...@gmail.com> wrote:> Hello, > > I have a transfer function from ARMA or AR model having some high order. I > want to obtain H(s). > My approach is to assume that H(s) will have a form that will result in a > high H(z) ARMA/AR model , and find a relation between these two!! > > I would appertiate any suggestion or comment,One way you might try, is to separate the ARMA model into biquads and then use the Bilinear Transform. Rune

Reply by ●June 17, 20092009-06-17

m.alawieh wrote:> Hello, > > I have a transfer function from ARMA or AR model having some high order. I > want to obtain H(s).Obtain H(S) in what sense? Least squares, equripple, BLT, IID ?> My approach is to assume that H(s) will have a form that will result in a > high H(z) ARMA/AR model , and find a relation between these two!!Ill problem and a bad idea to do that. H(Z) and H(S) are two different beasts. There can't be direct relationship. Especially as you are dealing with the ARMA models.> I would appertiate any suggestion or comment,Solve for the roots in Z domain, then map the roots to S domain. You will get the peculiar function in S domain which may not have to do anything with the original process. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com

Reply by ●June 17, 20092009-06-17

> > >m.alawieh wrote: > >> Hello, >> >> I have a transfer function from ARMA or AR model having some highorder. I>> want to obtain H(s). > >Obtain H(S) in what sense? Least squares, equripple, BLT, IID ? > >> My approach is to assume that H(s) will have a form that will result ina>> high H(z) ARMA/AR model , and find a relation between these two!! > >Ill problem and a bad idea to do that. H(Z) and H(S) are two different >beasts. There can't be direct relationship. Especially as you are >dealing with the ARMA models.Ill is the best word to describe it; I did it this way : let : 1-H(s)= b1/(a1+a2*s) + b2/(a3+a4*s) + b3/(a5+a6*s) + ... to increase ARMA model oder add more terms (proof by trail). 2- h(t)=InverseLapce(H(s)) 3- Ztransform(h(nT)) collect w.r.t 'z' ----> ARMA model Problem: the terms realting aram parameters with the derived looks really 'Ill' again. ****** I will say my model problem maybe I can get a good advice, I am making a model for clock errors resulting from oscillators behaviour. By finding this model i want to go next to a Kalman filter, to correct this errors. The approach was to find the transfer function using PSD parametric estimation. The measurement is the 1st derivative of the clk deviation. After finding H(z) for our system, i went to Kalman implementation. X_k=Phi*X_(k-1)+N but what am looking for is the clk deviation, and discrete X_k here is the derivative of it!!! So I thought the only way to get through this, is to find H(s) and characterize my system. Thanks