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12.1 Common z-transforms

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Common Continuous Time Fourier Series
Signal Z-transform Region of Convergence
δ ( t ) 1 all s
δ ( t - T ) e - ( s T ) all s
u ( t ) 1 s R > 0
- u ( - t ) 1 s R < 0
t u ( t ) 1 s 2 R > 0
t n u ( t ) n ! s n + 1 R > 0
- ( t n u ( - t ) ) n ! s n + 1 R < 0
e - ( λ t ) u ( t ) 1 s + λ R > - λ
( - ( e - ( λ t ) ) u ( - t ) 1 s + λ R < - λ
t e - ( λ t ) u ( t ) 1 ( s - λ ) 2 R > - λ
t n e - ( λ t ) u ( t ) n ! ( s + λ ) n + 1 R > - λ
- ( t n e - ( λ t ) u ( - t ) ) n ! ( s + λ ) n + 1 R < - λ
cos ( b t ) u ( t ) s s 2 + b 2 R > 0
sin ( b t ) u ( t ) b s 2 + b 2 R > 0
e - ( a t ) cos ( b t ) u ( t ) s + a ( s + a ) 2 + b 2 R > - a
e - ( a t ) sin ( b t ) u ( t ) b ( s + a ) 2 + b 2 R > - a
d n d t n δ ( t ) s n all s
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Source:  OpenStax, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15
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