# Hw3 - DIGITAL SIGNAL PROCESSING-I HOME WORK#3 Submitted by...

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DIGITAL SIGNAL PROCESSING-I HOME WORK #3 Submitted by Sriram Yarlagadda Sid # 2196944

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PROBLEM -1 GIVEN: System difference equation: y [ n ] 0.5 y [ n 1] 0.25 y [ n 2] 0.5 x [ n ] 0.5 x [ n 2] -------(1) Required : To compute the time domain impulse response Solution: ] 2 [ 5 . 0 ] [ 5 . 0 ] 2 [ 25 . 0 ] 1 [ 5 . 0 ] [ n x n x n y n y n y Applying Z transforms on both sides ]} 2 [ { 5 . 0 ]} [ { 5 . 0 ]} 2 [ { 25 . 0 ]} 1 [ { 5 . 0 ]} [ { n x Z n x Z n y Z n y Z n y Z ) ( 5 . 0 ) ( 5 . 0 ) ( 25 . 0 ) ( 5 . 0 ) ( 2 2 1 z X z z X z Y z z Y z z Y Y ( z ){1 0.5 z 1 0.25 z 2 } X ( z ){0.5 0.5 z 2 } Y ( z ) X ( z ) 0.5 0.5 z 2 1 0.5 z 1 0.25 z 2 H ( z ) 0.5 0.5 z 2 1 0.5 z 1 0.25 z 2 -------(2) Substitute z e j in equation 2 H ( e j ) 0.5 0.5 e 2 j 1 0.5 e j 0.25
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Hw3 - DIGITAL SIGNAL PROCESSING-I HOME WORK#3 Submitted by...

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