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Leo Lam © 2010-2012 Signals and Systems EE235
People types There are 10 types of people in the world: Those who know binary and those who don’t. Leo Lam © 2010-2012
Today’s menu From Friday: –Manipulation of signals –To Do: Really memorize u(t), r(t), p(t) Even and odd signals Dirac Delta Function
How to find LCM Factorize and group Your turn: 225 and 270’s LCM Answer: 1350 Leo Lam © 2010-2012
Even and odd signals Leo Lam © 2010-2012 An even signal is such that: t Symmetrical across the t=0 axis t Asymmetrical across the t=0 axis An odd signal is such that:
Even and odd signals Leo Lam © 2010-2012 Every signal sum of an odd and even signal. Even signal is such that: The even and odd parts of a signal Odd signal is such that:
Even and odd signals Leo Lam © 2010-2012 Euler’s relation: What are the even and odd parts of Even part Odd part
Summary: Even and odd signals Breakdown of any signals to the even and odd components Leo Lam © 2010-2012
Delta function δ(t) Leo Lam © 2010-2012 “a spike of signal at time 0” 0 The Dirac delta is: The unit impulse or impulse Very useful Not a function, but a “generalized function”)
Delta function δ(t) Leo Lam © 2010-2012 Each rectangle has area 1, shrinking width, growing height ---limit is (t)
Dirac Delta function δ(t) Leo Lam © 2010-2012 “a spike of signal at time 0” 0 It has height = , width = 0, and area = 1 δ(t) Rules 1.δ(t)=0 for t≠0 2.Area: 3. If x(t) is continuous at t 0, otherwise undefined 0 t0t0 Shifted to time instant t 0 :
Dirac Delta example Evaluate Leo Lam © 2010-2012 = 0. Because δ(t)=0 for all t≠0
Dirac Delta – Your turn Evaluate Leo Lam © 2010-2012 = 1. Why? Change of variable: 1
Scaling the Dirac Delta Proof: Suppose a>0 a<0 Leo Lam © 2010-2011
Scaling the Dirac Delta Proof: Generalizing the last result Leo Lam © 2010-2011
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
Leo Lam © Signals and Systems EE235 Leo Lam.
Leo Lam © Signals and Systems EE235 Oh beer… An infinite amount of mathematicians walk into a bar. The first one orders a beer. The second.
Leo Lam © Signals and Systems EE235. Leo Lam © Arthur’s knights Who was the largest knight at King Arthur’s round table? Sir Cumfrence,
Leo Lam © Signals and Systems EE235 Today’s Cultural Education: Liszt: Von der Wiege bis zum Grabe, Symphonic Poem No. 13.
Leo Lam © Signals and Systems EE235 Lecture 25.
Leo Lam © Signals and Systems EE235. Leo Lam © Happy Tuesday! Q: What is Quayle-o-phobia? A: The fear of the exponential (e).
Leo Lam © Signals and Systems EE235 Lecture 21.
Leo Lam © Signals and Systems EE235 October 14 th Friday Online version.
Finding the LCM Test #4 Question 1 Find the LCM of 3 and 5.
Leo Lam © Signals and Systems EE235. Fourier Transform: Leo Lam © Fourier Formulas: Inverse Fourier Transform: Fourier Transform:
Leo Lam © Signals and Systems EE235. Leo Lam © Today’s menu LTI System – Impulse response Lead in to Convolution.
Leo Lam © Signals and Systems EE235 KX5BQY.
Leo Lam © Signals and Systems EE235. Leo Lam © Pet Q: Has the biomedical imaging engineer done anything useful lately? A: No, he's.
In our lesson today we will learn how to find the area of a building.
Leo Lam © Signals and Systems EE235. Leo Lam © Breeding What do you get when you cross an elephant and a zebra? Elephant zebra sin.
Leo Lam © Signals and Systems EE235. Todays menu Leo Lam © Fourier Transform table posted Laplace Transform.
Leo Lam © Signals and Systems EE235. Leo Lam © Convergence Two mathematicians are studying a convergent series. The first one says:
Leo Lam © Signals and Systems EE235. Leo Lam © Today’s menu Today: Fourier Series –“Orthogonality” –Fourier Series etc.
SYMMETRY, EVEN AND ODD FUNCTIONS NOTES: 9/11. SYMMETRY, EVEN AND ODD FUNCTIONS A graph is symmetric if it can be reflected over a line and remain unchanged.
Leo Lam © Signals and Systems EE235 Leo Lam © Working with computers.
Leo Lam © Signals and Systems EE235 Lecture 22.
Example: cost of bananas at $0.19 each 0.19b Objective.
Leo Lam © Signals and Systems EE235. Leo Lam © Stanford The Stanford Linear Accelerator Center was known as SLAC, until the big earthquake,
Continuous-Time Convolution EE 313 Linear Systems and Signals Fall 2005 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian.
EECS 20 Chapter 9 Part 21 Convolution, Impulse Response, Filters In Chapter 5 we Had our first look at LTI systems Considered discrete-time systems, some.
Leo Lam © Signals and Systems EE235. Leo Lam © Surgery Five surgeons were taking a coffee break and were discussing their work. The.
Continuous-Time Convolution Impulse Response Impulse response of a system is response of the system to an input that is a unit impulse (i.e., a.
Chapter 2 Sections 5-6 Problem Solving and Formulas.
Leo Lam © Signals and Systems EE235. So stable Leo Lam ©
11-1 Areas of Rectangles and squares. Formulas 1) Area of rectangle = base x height or length X width 2) Area of square = (side) 2 or base X height 3)
Chapter 2 INTRODUCTION TO SIGNALS DeSiaMorewww.desiamore.com/ifm1.
Leo Lam © Signals and Systems EE235. Courtesy of Phillip Leo Lam ©
Created for ENMU Tutoring/Supplemental InstructionPeterson Fall 2011.
Chapter 1 -Discrete Signals A Sampled or discrete time signal x[n] is just an ordered sequence of values corresponding to the index n that embodies the.
Fourier Series For more ppts, visit
Expressions in Perimeter Problems. Suppose you are given the perimeter, and need to find the sides. Example: The perimeter of the rectangle is 66. –What.
Fourier Series. is the “fundamental frequency” Fourier Series is the “fundamental frequency”
(a) (b) (c) (d). What is (1,2,3) (3,4,2)? (a) (1, 2, 3, 4) (b) (1,2) (3,4) (c) (1,3,4,2) (d) (3,1) (4,2)
Leo Lam © Signals and Systems EE235. Summary: Convolution Leo Lam © Draw x() 2.Draw h() 3.Flip h() to get h(-) 4.Shift forward.
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