1. Leo Lam © 2010-2012 Signals and Systems EE235

2. Leo Lam © 2010-2011 Arthur’s knights Who was the largest knight at King Arthur’s round table? Sir Cumfrence, he got his size from eating too much pie.

3. Leo Lam © 2010-2011 Today’s menu To do –Lab starts soon! Dirac Delta Function (cont’) System properties –Linearity –Time invariance –Stability –Invertibility –Causality –Memory

4. Multiplication of a function that is continuous at t 0 by δ(t) gives a scaled impulse. Sifting Properties Relation with u(t) Summary: Dirac Delta Function Leo Lam © 2010-2011

5. Evaluate Dirac Delta – Another one Leo Lam © 2010-2011

6. Is this function periodic? If so, what is the period? (Sketch to prove your answer) Slightly harder Leo Lam © 2010-2011 Not periodic – delta function spreads with k 2 for t>0 And x(t) = 0 for t<0

7. Energy and power The energy of a signal Definition: An energy signal is any signal such that: Physically: this signal has finite energy Leo Lam © 2010-2011

8. Power The power of a signal Definition: A power signal is any signal such that: Physically: this signal has finite average power Leo Lam © 2010-2011

9. Signal power and energy What is the energy of u(t) Leo Lam © 2010-2011 Why?

10. Signal power and energy What is the power of u(t) Leo Lam © 2010-2011

11. Summary: Signal energy/power Defined Energy and Power of signals Defined Energy signal/Power signal Leo Lam © 2010-2011

12. System Leo Lam © 2010-2011 delay amplifier integrator sifter x(t)