GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 23 of 65

Marks: +1, -0

Which one of the following pole-zero plots corresponds to the function of an LTI system characterized by the input-output difference equation given below?

y[n]=∑↙{k=0}↖{3}(-1)^{k} x[n-k]

Validate

Solution:

{Y}( {n})=∑↙{ {K}=0}^{3}(-1)^{ {K}} {X}( {n}- {K})

{Y}( {n})= {X}( {n})- {X}( {n}-1)+ {X}( {n}-2)- {X}( {n}-3)

{Y}( {z})=1- {z}^{-1}+ {z}^{-2}- {z}^{-3}

{y}( {z})=\;{ {z}^{3}- {z}^{2}+ {z}^{1}-1}/{ {z}^{3}}

3 poles at

z=0

and number of zeros is 4
So the option (D) is correct

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