Introduction to Digital Signal and System Analysis - Tutorsindia
Introduction to Digital Signal and System Analysis - Tutorsindia
Introduction to Digital Signal and System Analysis - Tutorsindia
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<strong>Introduction</strong> <strong>to</strong> <strong>Digital</strong> <strong>Signal</strong> <strong>and</strong> <strong>System</strong> <strong>Analysis</strong><br />
Z Domain <strong>Analysis</strong><br />
They are plotted in Figure 5.4.<br />
Table 5.2 z-Transform pairs<br />
<strong>Signal</strong> x [n]<br />
Z-Transform X (z)<br />
δ [n]<br />
1<br />
u [n]<br />
z<br />
z −1<br />
z<br />
r [n]<br />
( z −1) 2<br />
a n u[n]<br />
( 1−<br />
a n ) u[<br />
n]<br />
z<br />
z − a<br />
z(1<br />
− a)<br />
( z − a)(<br />
z −1)<br />
( nΩ ) u[<br />
]<br />
z( z − cos Ω )<br />
cos<br />
0<br />
n<br />
( nΩ ) u[<br />
]<br />
sin<br />
0<br />
n<br />
( n ) u[<br />
]<br />
a n sin Ω<br />
0<br />
n<br />
z<br />
z<br />
z<br />
2<br />
2<br />
2<br />
− 2z<br />
cos Ω<br />
z sin Ω<br />
0<br />
− 2z<br />
cos Ω<br />
az sin Ω<br />
0<br />
− 2az<br />
cos Ω<br />
0<br />
0<br />
0<br />
0<br />
+ 1<br />
+ 1<br />
+ a<br />
2<br />
z-plane<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
-0.2<br />
-0.4<br />
-0.6<br />
-0.8<br />
-1<br />
-1 -0.5 0 0.5 1 1.5<br />
(a)<br />
Figure 5.4 Zeros <strong>and</strong> poles of the signal<br />
69<br />
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