(i) Determine impulse response of the system.

(ii) Determine step response of the system.

(iii) Plot pole-zero pattern and state whether system is stable.

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 10

Year : MAY 2014

(i) Impulse response of the system:

By z-transform,

$Y(z) = \dfrac34 z^{-1} Y(z)-\dfrac18 z^{-2} Y(z)+X(z) \\ Y(z) - \dfrac34 z^{-1} Y(z)+\dfrac18 z^{-2} Y(z) = X(z) \\ Y(z)(1- \dfrac34 z^{-1}+\dfrac18 z^{-2} ) = X(z) \\ H(z) = \dfrac{Y(z)}{X(z)} =\dfrac1{1- \dfrac34 z^{-1}+\dfrac18 z^{-2}} \\ H(z) = \dfrac{z^2}{z^2- \dfrac34 z+\dfrac18} \\ H(z) = …