Suppose I have a IIR filter represented by $$G_0\left(z\right)=\frac{1}{1-0.2z^{-1}-0.1z^{-2}}$$
I would like to use the LMS algorithm to model an FIR filter $G\left(z\right)$ of order $N = 15$ such that it would adaptively reach $ G_0\left(z\right)$ coefficients values
So we know that $G_0$ can be represented by:
num = 1;
den = [1; -0.2; -0.1];
my issue is that I don't know how to initiate $G(z)$ given its order is $N=15$.
Is it valid to say:
G(z) = zeros(N,1)??
because my confusion is that if $G_0(z)$ has only 3 coefficients, how would $G(z)$ converge to 3 coefficients given that it is 15 taps long?
Please give me some clear insights into this. Thank you in advance.