시스템공학

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Example 4. 1

Consider the signal From Eq. (4.2)

For convergence of we require that

Thus, the region of convergence is the range of values of z for which or,
equivalently, Inside the region of convergence the infinite siries converges to
(4.10)
Here we have used the familiar formula for the sum of terms of a geometric series. The
z-transform converges for any finite value of The Fourier transform of x[n], on the
other hand, converges only if For is the unit step sequence with
z=transform
(4.11)

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