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)
