1. Leo Lam © 2010-2011 Signals and Systems EE235

2. Leo Lam © 2010-2011 Laplace Examples A bunch of them

3. Standard Laplace question Find the Laplace Transform, stating the ROC. So: Leo Lam © 2010-2011 ROC extends from to the right of the most right pole ROC xxo

4. Inverse Laplace Example (2 methods!) Find z(t) given the Laplace Transform: So: Leo Lam © 2010-2011

5. Inverse Laplace Example (2 methods!) Find z(t) given the Laplace Transform (alternative method): Re-write it as: Then: Substituting back in to z(t) and you get the same answer as before: Leo Lam © 2010-2011

6. Inverse Laplace Example (Diffy-Q) Find the differential equation relating y(t) to x(t), given: Leo Lam © 2010-2011

7. Laplace for Circuits! Don’t worry, it’s actually still the same routine! Leo Lam © 2010-2011 Time domain inductor resistor capacitor Laplace domain Impedance!

8. Laplace for Circuits! Find the output current i(t) of this ugly circuit! Then KVL: Solve for I(s): Partial Fractions: Invert: Leo Lam © 2010-2011 R L +-+- Given: input voltage And i(0)=0 Step 1: represent the whole circuit in Laplace domain.

9. Step response example Find the transfer function H(s) of this system: We know that: We just need to convert both the input and the output and divide! Leo Lam © 2010-2011 LTIC

10. A “strange signal” example Find the Laplace transform of this signal: What is x(t)? We know these pairs: So: Leo Lam © 2010-2011 x(t) 1 2 3 2 1