How to compute poles-zeros using matlab?

H(z)=(1-2^-2)/(1-0.9*z^-1+0.6*z^-2+0.5*z^-3)
b=[1 0 -1 0];
a=[1 0.9 0.6 0.5];
% to find zeors
zeros=roots(b)
% to find poles 
poles=roots(a)
% to plot 
zplane(b,a)

Is my approach correct?

Answer 1

[Mathieu NOE]

hello

I hope the coefficient in b and a are correct (then the zeros and poles are inside the unit circle ) , because the first line is not 100% matching the coefficients you declared in b and a :

H(z)=(1-2^-2)/(1-0.9*z^-1+0.6*z^-2+0.5*z^-3) should be then replaced by :

H(z)=(1-z^-2)/(1+0.9*z^-1+0.6*z^-2+0.5*z^-3)

otherwise the zeros and pole computation is correct , and there is also this method (FYI) :

% alternative : 
[Z,P,K] = tf2zp(b,a)