Z transform pairs-2

Z transform pairs-2 - ECE306 z-TRANSFORM PROPERTIES The...

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z -TRANSFORM PROPERTIES The index-domain signal is x [ n ] for -∞ < n < ; and the z -transform is: X ( z ) = X n =-∞ x [ n ] z - n ⇐⇒ x [ n ] = 1 2 π j I X ( z ) z n dz z The ROC is the set of complex numbers z where the z -transform sum converges. Signal: x [ n ] -∞ < n < z -Transform: X ( z ) Region of Convergence x [ n ], x 1 [ n ] and x 2 [ n ] X ( z ) , X 1 ( z ) and X 2 ( z ) R x , R 1 and R 2 ax 1 [ n ] + bx 2 [ n ] aX 1 ( z ) + bX 2 ( z ) contains R 1 R 2 x [ n - n ] z - n X ( z ) R x except for the possible addition or deletion of z = 0or z =∞ z n x [ n ] X ( z / z ) | z | R x nx [ n ] - z dX ( z ) dz R x except for the possible addition or deletion of z = 0or z =∞ x * [ n ] X * ( z * ) R x < e { x [ n ] } 1 2 [ X ( z ) + X * ( z * ) ] contains R x = m { x [ n ] } 1 2 j [ X ( z ) - X * ( z * ) ] contains R x x [ - n ] X ( 1 / z ) 1 / R x ={ z : z - 1 R x } x 1 [ n ] * x 2 [ n ] X 1 ( z ) · X 2 ( z ) contains R 1 R 2 x 1 [ n
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Z transform pairs-2 - ECE306 z-TRANSFORM PROPERTIES The...

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