Example 9.1.  Find the z-transform of the unit pulse or impulse sequence   [Graphics:Images/ZTransformIntroMod_gr_76.gif].  

Solution 9.1.  This follows trivially from Equation (9-1)      

            [Graphics:Images/ZTransformIntroMod_gr_77.gif].  

 

[Graphics:Images/ZTransformIntroMod_gr_78.gif]

Explore Solution 9.1.

[Graphics:../Images/ZTransformIntroMod_gr_79.gif]




[Graphics:../Images/ZTransformIntroMod_gr_80.gif]

[Graphics:../Images/ZTransformIntroMod_gr_81.gif]

 

 

 

We are done.

Aside.  We can easily find the inverse of  X[z].

[Graphics:../Images/ZTransformIntroMod_gr_82.gif]




[Graphics:../Images/ZTransformIntroMod_gr_83.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell