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Q#1 Z Transform GATE EC 1997 MSQ +2 marks -0 marks

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In the figure is a linear time invariant discrete system is shown. Blocks labelled D represent unit delay elements. For , you may assume that , ,  are all zero.

(a) Find the expression for  and  in terms of x(n)

(b) Find the transfer function  in the z – domain

(c) If , find

(a)
\(\scriptstyle {y_1[n] + 2y_1[n-1] + y_1[n-2] = x[n-1]}\)

\(\scriptstyle {y_2[n] = x[n-2] - 2y_2[n-1] - y_2[n-2]}\)

(b)
\(\scriptstyle {\frac{Y_2(z)}{X(z)}  = \frac{1}{[z+1]^2}}\)

(c) \(\scriptstyle {y_2[n] = (n-1)(-1)^{n-1} u[n-1]}\)

(c) \(\scriptstyle {y_2[n] = (n+1)(-1)^{n-1} u[n+1]}\)

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