correlated interference related to gaussian autoregressiv

how can i generate the sequence of following equation

phi1=1.98;

phi2=-0.9801;

I(k)=phi1*i(k-1)+phi2*i(k-2)+e(k)

k=2:100

....i(-1),i(-2)......<0 are equal to zero

e(k)=white gaussian noise with variance 0.01

Answer 1

[Mathieu NOE]

hello

weel, you where not very far from the code....

here is it

NB that the for loop start at indice 3 because matlab works with indices starting at 1 and not zero

phi1=1.98;
phi2=-0.9801;
samples = 100;

e = randn(samples,1);  % e(k)=white gaussian noise with variance 0.01
v = var(e);  % check variance
v_target = 0.01;
amp = sqrt(v_target/v); % compute amplitude factor correction to get target variance
e = e*amp; 
v = var(e)  % now we have the correct variance

v = 0.0100

% init I
I(1) = e(1);         % ....i(-1),i(-2)......<0 are equal to zero
I(2) = phi1*I(1)+ 0 +e(2);

% main loop
for k=3:samples
    I(k) = phi1*I(k-1)+phi2*I(k-2)+e(k);
end

plot(I);