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

2. Leo Lam © 2010-2011 Surgery Five surgeons were taking a coffee break and were discussing their work. The first said, "I think accountants are the easiest to operate on. You open them up and everything inside is numbered.“ The second said, "I think librarians are the easiest to operate on. You open them up and everything inside is in alphabetical order.“ The third said, "I like to operate on electricians. You open them up and everything inside is color-coded.“ The fourth one said, "I like to operate on lawyers. They're heartless, spineless, gutless, and their heads and their butts are interchangeable." Fifth surgeon said, "I like Engineers...they always understand when you have a few parts left over at the end..."

3. Leo Lam © 2010-2011 Today’s menu Lab 3 this week (posted) Homework 2 due tomorrow Homework 1 issues Convolution

4. Convolution Integral Leo Lam © 2010-2011 4 Standard Notation The output of a system is its input convolved with its impulse response

5. Quick recap Leo Lam © 2010-2011 5 x(t) is the sum of the weighted shifted impulses

6. Convolution integral Leo Lam © 2010-2011 6 Function of  =h(- (-t)) Function of  shifted by t , not t

7. Convolution integral Leo Lam © 2010-2011 7 Two ways to evaluate: –Mathematically –Graphically For graphical convolution, see demo in Riskin interactive notes (lesson 6, lesson 7)

8. Convolution (mathematically) Leo Lam © 2010-2011 8 Use sampling property of delta: Evaluate integral to arrive at output signal: Does this make sense physically?