(→Time Shifting) |
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| Line 8: | Line 8: | ||
==Convolution== | ==Convolution== | ||
:<math>x_{1}(t)*x_{2}(t) =L=> X_{1}(s)X_{2}(s) </math>, RoC contains R1 and R2 | :<math>x_{1}(t)*x_{2}(t) =L=> X_{1}(s)X_{2}(s) </math>, RoC contains R1 and R2 | ||
| + | Corollary: | ||
| + | :x(t) => h(t) => x(t)*h(t) | ||
Latest revision as of 13:48, 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
Corollary:
- x(t) => h(t) => x(t)*h(t)
