Two discrete-time linear time-invariant systems with impulse responses {h}_{1}[ {n}]=\delta[ {n}-1]+\delta[ {n}+1] and {h}_{2}[ {n}]=\delta[ {n}]+\delta[ {n}-1] are connected in cascade, where \delta[ {n}] is the Kronecker delta. The impulse response of the cascaded system is:

Correct Answer is : δ[n−2]+δ[n−1]+δ[n]+δ[n+1]

\delta[ {n}] \delta[ {n}-1]+\delta[ {n}-2] \delta[ {n}+1]

\delta[ {n}-2]+\delta[ {n}-1]+\delta[ {n}]+\delta[ {n}+1]

\delta[ {n}-1] \delta[ {n}]+\delta[ {n}+1] \delta[ {n}-1]

GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 16 of 65

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Two discrete-time linear time-invariant systems with impulse responses

{h}_{1}[ {n}]=δ[ {n}-1]+δ[ {n}+1]

and

{h}_{2}[ {n}]=δ[ {n}]+δ[ {n}-1]

are connected in cascade, where

δ[ {n}]

is the Kronecker delta. The impulse response of the cascaded system is:

Solution:

{h}_{1}[ {n}]=δ[ {n}-1]+δ[ {n}+1]

{h}_{2}[ {n}]=δ[ {n}]+δ[ {n}-1]

{h}_{1}[ {n}] * {h}_{2}[ {n}]=δ[ {n}-1]+δ[ {n}-2]+δ[ {n}+1]+δ[ {n}]

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