Leo Lam © Signals and Systems EE235

Leo Lam © 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.

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

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 ©

Evaluate Dirac Delta – Another one Leo Lam ©

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

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 ©

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

Signal power and energy What is the energy of u(t) Leo Lam © Why?

Signal power and energy What is the power of u(t) Leo Lam ©

Summary: Signal energy/power Defined Energy and Power of signals Defined Energy signal/Power signal Leo Lam ©

System Leo Lam © delay amplifier integrator sifter x(t)