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Dig Sig Proc&Analys

by: Ophelia Ritchie

Dig Sig Proc&Analys EECS 451

Ophelia Ritchie
GPA 3.8


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Class Notes
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This 1 page Class Notes was uploaded by Ophelia Ritchie on Thursday October 29, 2015. The Class Notes belongs to EECS 451 at University of Michigan taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/231537/eecs-451-university-of-michigan in Engineering Computer Science at University of Michigan.

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Date Created: 10/29/15
EECS 451 1 SIDED Z TRANSFORM DEF Zxn Xz 200 xnz n even if is noncausal Compare to 2sz ded Z transforrn Xz 2730700 WHY To solve difference equations With nonzero initial conditions in PROPERTIES OF 1SIDED ZTRANSFORM Xz causal gt1 sided Z transforrn X 22 sided Z transforrn X Unique inverse only for causal signals no info on lt 0 Equal causal parts but unequal anticausal parts gtsarne X Z 3 ROC Always gt lpmml largest pole of Xz so don t bother 4a D gt 0 gt zxn 17 z DXz 251 x nz 4b D gt 0 gt zxn 17 zDXz 25 my i Shift right gtrnust add in terms previously anticausal ii Shift left gtrnust subtract off terrns now anticausal iii Compare to Cfl2733 82X8 80 60 NH SOLVING DIFFERENCE EQNS WITH INITIAL CONDITIONS Solve 2yn 3yn 1 yn 2 un 1 un 2 Chen p264 Take 2 2Yz 3z 1Yz y 1z z 2Yz y 1z y 2 22 2 3271 z 2Yz 3y 1 y 2 z 1y 1 1 z 1 2 Uz 1 z 1 Z Z 3y 1 y 2 z 1y 1 i Solve Y i 2 3Z4 Z72 Uz 2 32471 Z72 zeroistate response zeroiinput response Plug in ununit step gt Uz Uz 17 4 y 1 2y 2 1 t 7 1Z 172 2 522 1 74 42 1z2 Y 7 2327127217271 23271272 2lt15271X1271gtlt17271gt YZ S Il 13 112 Note no constant term 4 1 7 1 3 1 Mn un 1nun 6um natural response forced


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