Modeling and simulating a signal with an autoregressive model

Hello

I want to model a signal with an autoregressive model using Matlab. So by taking the data Y, I was able to estimate using Matlab:

• The parameters a1, a2, ..., ap and the variance of white noise by using the Yule-Walker
• And the optimal order p of the model using the FPE or AIC criterion.

My problem is: the signal that I could simulate using this code:

    for t=1:N
         arp=0;
         for j=1:p
            if t > j
                arp = arp + A(j)*X(t-j);
            end
         end
         X(t) = arp + u(t);
     end

     with: u = white noise and A = (a1,...,ap)

is not appropriate to the used data Y.

In other words, the obtained simulation result X (model) does not resemble to the the given signal Y.

Is there a solution to find a good simulation of the used model?

[sai lakshmi]

Mr.Ayech Did you get your simulated signal using auto regressive model,I am working on that concept,could you suggest me please!

[juan gomez]

you can find the parameters a1, a2...ap with aryule that works with yule w

after that you can conv you signal with the vector of the parameters to have the noise that you will use as input for the filter. After that you use filter with 1 and the parameters as H(z) and the noise as input and the output is the new signal AR

Answer 1

[Honglei Chen]

Hi Walid,

If you know parameter a1,a2,..,ap, I think the simplest way to simulate an AR process is

1. Create an IIR filter with coefficients a1,a2,..,ap 2. Pass the white noise through this filter to obtain X

You should be able to find details in most spectral analysis book, such as Kay's Modern Spectral Estimation.

HTH