EE3TP4_Z_TransformProperties_2_v1_Lecture 35

# EE3TP4_Z_TransformProperties_2_v1_Lecture 35 - [ X z x [ ]]...

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Z Transform Properties Linearity Right shift (causal and non-causal signal cases) Convolution x [ n ]∗ h [ n ] ↔ X z H z x [ n q ] ↔ z q X z  x [− 1 ] z q 1 x [− 2 ] z q 2 ... z 1 x [− q 1 ] x [− q ] a x [ n ] bh [ n ] ↔ a X z  b H z Let's look at some others!

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Left Shift Property x [ n ] ↔ X z x [ n 1 ] ? What happens to the Z Transform if we shift a function to the left?
n z 5 z 4 z 3 z 2 z 1 z 0 z -1 z -2 z -3 z -4 z -5 z -6 x[-5] x[-4] x[-3] x[-2] x[-1] x[0] x[1] x[2] x[3] x[4] X z = n = 0 x [ n ] z n = x [ 0 ] z 0 x [ 1 ] z 1 x [ 2 ] z 2 ⋯

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Left Shift Property x [ n ] ↔ X z x [ n 1 ] ↔ z

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Unformatted text preview: [ X z x [ ]] n z 5 z 4 z 3 z 2 z 1 z z-1 z-2 z-3 z-4 z-5 z-6 X z = n = x [ n ] z n = x [ ] z x [ 1 ] z 1 x [ 2 ] z 2 x[-5] x[-4] x[-3] x[-2] x[-1] x[0] x[1] x[2] x[3] x[4] e.g. x [ n ]= 0 for n 2. Form x [ n 2 ] . Therefore x [ n 2 ] z 2 X z n m a n m z z a m 1 or Why is this result important?...
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## This note was uploaded on 02/01/2011 for the course ECE 3TP4 taught by Professor Drterrencetodd during the Fall '10 term at McMaster University.

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EE3TP4_Z_TransformProperties_2_v1_Lecture 35 - [ X z x [ ]]...

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