Can matlab give me difference equation from transfer fucntion

Hi My transfer function is H(z)= (1-z(-1)) / (1-3z(-1)+2z(-2))

How can i calculate its difference equation. I have calculated by hand but i want to know the methods of Matlab as well

Answer 1

[Wayne King]

I think I'm trying to say that you see it right away if you have the Z-transform. Do you have the System Identification Toolbox? You can do:

M = idpoly([1 -3 2],[1 -1],'NoiseVariance',0)

[moonman]

Ok for this equation it is ok

lets suppose we have some complex transfer function

then is there any way matlab gives difference equation

[Ben Le]

Hi, If I don't have System Identification Toolbox, how can I do it in Matlab? Thanks.

Answer 2

[Gert Kruger]

syms z;

H = (1-z^-1) / (1-3*z^-1+2*z^-2);

[N, D] = numden(H);

Nc = eval(coeffs(N)); %Get coeffs and evaluatle symbolic variable, i.e. make real matrix

Dc = eval(coeffs(D));

Nc = Nc./(Dc(1)); %Turn into proper polynomial, first coeffs of a is 1

Dc = Dc./(Dc(1));

M = idpoly(Dc, Nc, 'NoiseVariance',0)

Answer 3

[Wayne King]

You have the difference equation:

H(z)= (1-z(-1)) / (1-3z(-1)+2z(-2))

y(n)-3*y(n-1)+2*y(n-2) = x(n)-x(n-1);

zplane([1 -1],[1 -3 2]);

This is not stable, you have a pole outside the unit circle.

[moonman]

And Thanks for telling me abt new command zplane

I used to use pzmap which does not show overlapped poles and zeros but zplane is showing the digits if multiple poles and zeros are there at same place

Great help

Answer 4

[moonman]

Thanks king yes i have calculated all this and i know it is unstable systm but i need to know that can matlab give difference equation the way it gives poles and zeros by pole zero command and plots by pzmap