Laplace Transform 1.1

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COMMON DATA QUESTIONS

For the LTI system described by the equation: $y(n)= y(n-1)+y(n-2)+x(n-1)$

(i) Determine the transfer function $G(z)= \frac{Y(z)}{X(z)}$
(a)$ \frac{z}{(z^2-z-1)}$
(b)$\frac{z-1}{(z^2+z-1)}$
(c)$\frac{z+2}{(z^2-z-2)}$
(d)none of above

(ii) The poles of the transfer function G(z) are
(a)$0.5 - 0.5√5 , .5+0.5√5$
(b)$1-√5 , 1+√5$
(c)$1 , -2$
(d) insufficient data

(iii)Determine the ROC and derive the consequent information regarding the system stability
(a)ROC is |z| > 0.5+0.5√5, system is unstable
(b)ROC is |z|<0.5+0.5√5 system is stable
(c)ROC is |z| > 2 , system is unstable
(d)cannot determine

Answer for (i) is ( a )
Answer for (ii) is ( a )
Answer for (iii) is ( a )

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