(New page: ===Properties of Laplace Transform=== ==Time Shifting== <math> X(t-t0) -> e^{-st_{0})X(s) <\math>, RoC unchanged) |
(→Time Shifting) |
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==Time Shifting== | ==Time Shifting== | ||
| − | <math> | + | :<math> x(t-t0) =L=> e^{-st_{0}}X(s) </math>, RoC unchanged |
| + | :<math> e^{s_{0}t}x(t) =L=> X(s-s_{0}) , RoC (S-S_{0} | SeR) </math> | ||
| + | ==Time Scaling== | ||
| + | :<math> x(at) =L=> (1/|a|)X(s/a) </math>, RoC = {as|SeR} | ||
| + | ==Convolution== | ||
| + | :<math>x_{1}(t)*x_{2}(t) =L=> X_{1}(s)X_{2}(s) </math>, RoC contains R1 and R2 | ||
Revision as of 13:46, 23 November 2008
Properties of Laplace Transform
Time Shifting
- $ x(t-t0) =L=> e^{-st_{0}}X(s) $, RoC unchanged
- $ e^{s_{0}t}x(t) =L=> X(s-s_{0}) , RoC (S-S_{0} | SeR) $
Time Scaling
- $ x(at) =L=> (1/|a|)X(s/a) $, RoC = {as|SeR}
Convolution
- $ x_{1}(t)*x_{2}(t) =L=> X_{1}(s)X_{2}(s) $, RoC contains R1 and R2
