The transfer function of a stable discrete time LTI system is {H}( {z})= { {K}( {z}-\alpha)}/{ {z}+0.5}, where {K} and {a} \to real no. The value of {a}=? with | {a}|>1, for which magnitude rest one of the system to constant over all frequency.

GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 40 of 65

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The transfer function of a stable discrete time LTI system is

{H}( {z})=\;{ {K}( {z}-α)}/{ {z}+0.5}

, where

{K}

and

{a} →

real no. The value of

{a}=?

with

| {a}|>1

, for which magnitude rest one of the system to constant over all frequency.

Solution:

Magnitude will become constant for all pass system

{H}( {z})=\;{ {Z}- {a}}/{ {Z}+ {b}}

{b}=\;{1}/{α^{*}}

α=\;{1}/{0.5}

{a}=2

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