Simple Filter representation in Matlab

Question

Suppose I have an IIR filter in the $z$-domain in the following form: $$ H\left(z\right)=\frac{1}{1-0.2z^{-1}-0.1z^{-2}} $$

How do I represent this in MATLAB?

I am pretty sure if I just listed the coefficients as H = [1 -0.2 -0.1]; this would be considered wrong. Can somebody help me with this please?

Answer 1

MATLAB assumes that the transfer function has a form like this:

$$ H(z) = \frac{b_0 + b_1z^{-1} + \ ... \ + b_{M}z^{-M}}{1+a_1z^{-1}+ \ ... \ + a_{N}z^{-N}} $$

So then you can read off the coefficients from your equation as $b_0=1$, $a_0=1$ (always assumed), $a_1 = -0.2$, and $a_2 = -0.1$. In MATLAB world, you define the coefficients as:

b = 1;
a = [1; -0.2; -0.1];

Further, if you wanted to actually use the filter on some signal, you can call the in-built function:

filterOutput = filter(b, a, filterInput);

Answer 2

You have to define numerator and denominator polynomials. In your case you have

b = 1;
a = [1,-0.2, -0.1];