Signals and Systems - Electrical Engineering

9.4 One-Sided Z-Transform 527

− 2 0 2

− 1

0

1

Real part

Imaginary part

0 5 10 15 20

h^2

(n

)

− 1

0

1

n

− 2 0 2

− 1

0

1

Real part

Imaginary part

0 5 10 15 20

0

0.5

1

h^1

(n

)

n

(a)

(b)

(c)

(d)

Imaginary part

0510 15 20

h^3

(n

)

− 1

0

1

n

− 2 0

2

2

− 1

0

1

Real part

− 3 − 2 − 1 0 1 2 3

− 1

0

1

2

Imaginary part

0510 15 20

h^4

(n

)

− 50

0

50

Real part n

FIGURE 9.3
Effect of pole location on the inverse Z-transform: (a) if the pole is atz= 1 the signal isu[n], constant forn≥ 0 ;
(b) if the pole is atz=− 1 the signal is a cosine of frequencyπcontinuously changing, constant amplitude; (c, d)
when poles are complex, if inside the unit circle the signal is a decaying modulated exponential, and if outside
the unit circle the signal is a growing modulated exponential.