$H(z)=\frac{1-z^{-1}}{(1-0.2z^{-1} -0.15z^{-2)}}$

1.Find the difference equation

2.Draw Direct Form-I and Direct Form-II realization structure.

3.Draw cascade form, parallel form realization.

The difference can be obtained by taking IZT if H(z)

$H(z)=\frac{(Y(z))}{(X(z))}$

$\frac{(Y(z))}{(X(z))}=\frac{(1-z^{-1})}{(1-0.2z^{-1}-0.15z^{-2} )}$

$Y(z)(1-0.2 z^{-1}-0.15z^{-2} )=X(z)(1-z^{-1})$

$Y(z)-0.2z^{-1} Y(z)-0.15z^{-2} Y(z)=X(z)-z^{-1} X(z)$

$Y(z)=X(z)-z^{-1} X(z)+0.2z^{-1} Y(z)+0.15z^{-2} Y(z)$

Taking inverse Z transform

$∴y(n)=x(n)-x(n-1)+0.2y(n-1)+0.15y(n-2)$

ii) Direct form-I and Direct form-II realization structure:

iii) Cascade form, parallel form realization cascade form:

$H(z) = \frac{1-z^{-1}}{(1-0.5z^{-1})(1+0.3z^{-1})}$

In cascade …