How to generate 100 sample data using the AR(1) model?

[meto]

how to generate 100 sample data using the AR(1) model?I have generated but I don't know this code is true or not.And also how can i calculate the autocorrelation matrix?

"a=0.5;
n=0.001;
x(1)=100;
for k=2:100
x(k)=a*x(k-1)+n;
end"

 

[artsil23]

Re: AR(1) model

100 samples are few, but well here is a code with a white noise in the input and the sistem is a AR of order 1


% generate white noise
Fm=25;
w=randn(4*Fm,1); %100 samples of noise
k=-50:50;
a=0.8;
%generate the output of the filter AR process H(z)=1/(1-az^(-1))

x=filter(1,[1 -a],w);

% we get the correlations

rxb0=xcorr(x(1:51),'biased');
rxteo=1/(1-a^2).*a.^abs(-50:50); theoretical correlation

figure(1);clf;
plot(k,rxteo); title('theoric correlation');grid on;

pause;hold on
%biased correlation
plot(k,rxb0,'r'); title('Biased Correlation');

% shift the fft

Sxb0=fft(ifftshift(rxb0));

f=[0:0.5/100:0.5*(1-1/100)]*Fm;
Sxteo=abs(1./fft([1 -a],100)).^2;
figure(2);clf; %Theoric
plot(f,10*log10(real(Sxteo(1:100))));grid on;title('Theoretical Spectral Dentisty Power');
pause; hold on
%biased
plot(f,10*log10(real(Sxb0(1:100))),'r');title('Spectral Dentisty Power');



or you can use [a e]=aryule[x,1]

Regards