leo lam © 2010-2011 signals and systems ee235. leo lam © 2010-2011 surgery five surgeons were...

Leo Lam © 2010-2011

Signals and Systems

EE235

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..."

Leo Lam © 2010-2011

Today’s menu

• Lab 3 this week (posted)• Homework 2 due tomorrow• Homework 1 issues

• Convolution

Leo Lam © 2010-2011

Convolution Integral

4

( ) ( )* ( ) ( ) ( )y t x t h t x h t d

Standard Notation

The output of a system is its input convolved with its impulse response

Leo Lam © 2010-2011

Quick recap

5

x(t) is the sum of the weighted shifted impulses

Leo Lam © 2010-2011

Convolution integral

6

( ) ( )* ( ) ( ) ( )y t x t h t x h t d

Function of

=h(- (-t)) Function of shifted by t

, not t

Leo Lam © 2010-2011

Convolution integral

7

• Two ways to evaluate:– Mathematically– Graphically

• For graphical convolution, see demo in Riskin interactive notes (lesson 6, lesson 7)

( ) ( )* ( ) ( ) ( )y t x t h t x h t d

Leo Lam © 2010-2011

Convolution (mathematically)

8

Use sampling property of delta:

Evaluate integral to arrive at output signal:

Does this make sense physically?