
The z-transform of a causal discrete-time signal f
k
, k ¼0, 1, 2, 3, . . . denoted F(z)orz{f
k
}is
defined by the infinite series
F(z) ¼ z{f
k
} ¼
X
1
k¼0
f
k
z
k
(4:352)
The region of convergence of F(z) in the z-plane is all complex numbers greater than a certain
distance from the origin, that is, jzj> R where R depends on the particular sequence of numbers
(discrete-time signal) f
k
(Kuo 1980). As in the case of the Laplace transformation, the region of
convergence of the z-transform for a particular discrete-time signal is of passing interest. The main
consideration is that the sum in Equation 4.352 converges to a complex number somewhere in the
z-plane. Several ...