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3.2 Table of common z-transforms

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Lists the z-transform and region of convergence (ROC) for several common discrete-time signals.

The table below provides a number of unilateral and bilateral z-transforms . The table also specifies the region of convergence .

The notation for z found in the table below may differ from that found in other tables. For example, the basic z-transform of u n can be written as either of the following two expressions, which are equivalent:
z z 1 1 1 z -1

Signal Z-Transform ROC
δ n k z k All z
u n z z 1 z 1
u n 1 z z 1 z 1
n u n z z 1 2 z 1
n 2 u n z z 1 z 1 3 z 1
n 3 u n z z 2 4 z 1 z 1 4 z 1
α n u n 1 z z α z α
α n u n z z α z α
n α n u n α z z α 2 z α
n 2 α n u n α z z α z α 3 z α
k 1 m n k 1 α m m α n u n z z α m 1
γ n α n u n z z γ α z 2 2 γ α z γ 2 z γ
γ n α n u n z γ α z 2 2 γ α z γ 2 z γ
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Source:  OpenStax, Intro to digital signal processing. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10203/1.4
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