Obtain the direct form I, direct form II, cascade and parallel form realization for the system y(n)= - 0.1y(n - 1)+0.2y(n - 2)+3x(n)+ 3.6x(n - 1)+0.6x(n

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written 2.4 years ago by

prajapatijaimin • 3.3k

Solution:

Let $3 x(n)+3.6 x(n-1)+0.6 x(n-2)=w(n)$

$y(n)=-0.1 y(n-1)+0.2 y(n-2)+\omega(n) .\\$

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Direct from,

$A(z)=\frac{Y(z)}{X(z)}=\frac{3+3.6 z^{-1}+0.6 z^{-2}}{1+0.1 z^{-1}-0.2 z^{-2}}\\$

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Cascade form,

$\begin{aligned}\\ &H(z)=\frac{\left(3+0.6 z^{-1}\right)\left(1+z^{-1}\right)}{\left(1+0.5 z^{-1}\right)\left(1-0.4 z^{-1}\right)} \\\\ &H_1(z)=\frac{3+0.6 z^{-1}}{1+0.5 z^{-1}} \text { and } H_2(z)=\frac{1+z^{-1}}{1-0.4 z^{-1}} .\\ \end{aligned}\\$

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Parallel form.

$H(z)=-3+\frac{7}{1-0.4 z^{-1}}+\frac{1}{1+0.5 z^{-1}}\\$

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