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I am new to the topic of system identification and looking for a large Autoregressive (AR) model. Can anybody point out a large stable AR model which has more than 2 coefficients AND there should be a large number of zero coefficients?

This link presents an example of how to have nonzero coefficients in lag 1,4 for order, $p=4$ AR(4) model. But, the values are NaN !! So, how do I apply this technique so as to generate a large AR model with more number of zero coefficients and lesser number of non-zero coefficients ?

EDIT:

Looking for any stable AR($p$) model (preferably popular cited ones, if available) of higher order $p \ge 20$ where the number of non-zero coefficients are few (constraint) . If I generate a noisy sinusoidal wave given below, then

%Generate sine wave = A*sin(2*pi*f*t + phi)
t = linspace(0,1,1000);
A = 5;
f = 2;
phi = pi/8;
sinewave = A*sin(2*pi*f*t + phi);
noisy_sine=sinewave+0.5*randn(size(t));
subplot(1,2,1);
plot(t, sinewave)
hold on;
subplot(1,2,2);
plot(t,noisy_sine);

%Generate AR model
order =20;
ARCoeff = aryule(noisy_sine,order);

It returns AR model of 20 lags. But, all the coefficients are non-zero. How do I generate AR model of any order higher than 2 where the number of non-zero coefficients are lesser than the number of zero coefficients ?

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  • $\begingroup$ It's simple to generate an AR(p) model of almost any arbitrary order. Will you consider it stable if it's slightly damped, but "lives" for at least 10k+ iterations (samples)? I can describe the method and provide an example. $\endgroup$ – werediver Apr 24 '14 at 13:40
  • $\begingroup$ mathworks.com/help/signal/ref/aryule.html provides example how to generate AR(4) model where the filter coefficients are provided. How do I get to know filter coefficients for filter order p=20,50,100? I have no experimental data, and was wondering to use rand. Could you kindly describe how I can generate large AR models? $\endgroup$ – SKM Apr 24 '14 at 18:13
  • $\begingroup$ Just take any data and fit the AR model to it. In the example you refered to replace aryule(y,4); with aryule(y,100);. Consider using a noisy combination of sinusoids as data. $\endgroup$ – werediver Apr 24 '14 at 19:11
  • $\begingroup$ Thank you, how do I make a noisy combination of sinusoids as data?Could you please let me know this?In general, what is the method of first knowing the filter coefficients /transfer function technicalities connected to signal processing as is given in the link? $\endgroup$ – SKM Apr 24 '14 at 19:20
  • $\begingroup$ Wait, do you need any (stable) AR(p) model or an AR(p) model with some predefined properties? Please, describe your requirements (feel free to extend your question post). $\endgroup$ – werediver Apr 24 '14 at 19:24
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I was able to produce the AR(p) model with much of zero-coefficients. I use Scilab rather than Matlab, therefore I'll just describe the technique:

  • Generate some appropriate data with the desired spectral properties - the AR model will mimic these spectral properties.
  • Fit the AR model of the desired order to your data.
  • Find the desired number of the coefficients with the lowest values and reset them to zero
    (something like a(find(abs(a) < stdev(a) / 2)) = 0 - valid in Scilab).

The resulting model should (may?) still has a similar spectral properties & satisfy your requirements considering zero-coefficients.

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