6.003: Signals and Systems. Lecture 1 Introduction to Signals and Systems
|
|
|
- Jonathan Dickerson
- 5 years ago
- Views:
Transcription
1 6.003: Signals and Sysems Lecure 1 Inroducion o Signals and Sysems
2 6.003: Signals and Sysems Today s handous: Single package conaining Subjec Informaion Lecure #1 slides (for oday) Reciaion #2 handou (for omorrow) Lecurer Insrucors Head TA TAs Secreary Tex Web Sie Denny Freeman (freeman@mi.edu) Qing Hu, Jeff Lang, Karen Livescu, Sanjoy Mahajan, Anonio Torralba Demba Ba (demba@mi.edu) Paul Azunre, Dheera Venkaraman, Keng-Hoong Wee, Seve Zhou Janice Balzer (balzer@mi.edu) Signals and Sysems by Oppenheim and Willsky mi.edu/6.003
3 6.003: Signals and Sysems Homework: where subjec maer is/isn learned. equivalen o pracice in spors or music. Weekly Homework Assignmens Convenional Homework Problems plus Engineering Design Problems (ofen using Malab, Ocave, or Pyhon) Homework Assignmens are longer (by abou 3 hours) han homework assignmens in 12 uni subjecs! 15 unis + 4 Engineering Design Poins Open Office Hours! Saa Basemen (32-044) Mondays and Tuesdays, afernoons and evenings
4 6.003: Signals and Sysems Collaboraion Policy Discussion of conceps in homework is encouraged Sharing of homework or code is no permied and will be repored o he COD Firm Deadlines Homework mus be submied in reciaion on due dae Lae homework will NOT be acceped unless excused by he saff, a Dean, or Physician Homework Exension Policy Every suden ges one exension Can be used for any weekly homework assignmen and for any reason Simply ask your TA for an exension before 11:59 pm on he day preceding he due dae (canno be rescinded)
5 6.003 Calendar Basic Represenaions of Discree-Time Sysems (4 weeks). difference equaions, block diagrams, operaor expressions, funcions, feedback and conrol, Z ransforms, convoluion (O&W Chapers 1, 2, 10, and 11). Basic Represenaions of Coninuous-Time Sysems (3 weeks). differenial equaions, block diagrams, operaor expressions, funcions, feedback and conrol, Laplace ransforms, convoluion (O&W Chapers 1, 2, 9, and 11). Signal Processing (2 weeks). Fourier Series, Fourier Transforms, Filering (O&W Chapers 3, 4, 5, and 6). Sampling (2 weeks). Sampling, aliasing, DT processing of CT signals (O&W Chaper 7). Communicaions (2 weeks). modulaion, AM, FM (O&W Chaper 8).
6 6.003: Signals and Sysems Weekly meeings wih class represenaives help saff undersand suden perspecive learn abou eaching One represenaive from each secion (6 oal) Tenaively mee on Thursday afernoon Ineresed?...send o freeman@mi.edu
7 Lecure 1: The Absracion signal in signal ou absracion: describe a (physical, mahemaical, or compuaional) by he way i ransforms inpus ino oupus.
8 Example: Mass and Spring
9 Example: Mass and Spring
10 Example: Mass and Spring
11 Example: Mass and Spring
12 Example: Mass and Spring
13 Example: Mass and Spring
14 Example: Mass and Spring
15 Example: Mass and Spring
16 Example: Mass and Spring x() y() x() mass & spring y()
17 Example: Mass and Spring x() y() x() mass & spring y()
18 Example: Mass and Spring x() y() x() mass & spring y()
19 Example: Mass and Spring x() y() x() mass & spring y()
20 Example: Mass and Spring x() y() x() mass & spring y()
21 Example: Mass and Spring x() y() x() mass & spring y()
22 Example: Mass and Spring x() y() x() mass & spring y()
23 Example: Mass and Spring x() y() x() mass & spring y()
24 Example: Mass and Spring x() y() x() y() mass & spring
25 Example: Mass and Spring x() y() x() y() mass & spring
26 Example: Mass and Spring x() y() x() y() mass & spring
27 Example: Mass and Spring x() y() x() y() mass & spring
28 Example: Mass and Spring x() y() x() y() mass & spring
29 Example: Mass and Spring x() y() x() y() mass & spring
30 Example: Mass and Spring x() y() x() y() mass & spring
31 Example: Mass and Spring x() y() x() y() mass & spring
32 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
33 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
34 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
35 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
36 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
37 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
38 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
39 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
40 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
41 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
42 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
43 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
44 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
45 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
46 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
47 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
48 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
49 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
50 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
51 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 0 () ank r 2 ()
52 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
53 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
54 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
55 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
56 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
57 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
58 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
59 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
60 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
61 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
62 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
63 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
64 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
65 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
66 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
67 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
68 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
69 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
70 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
71 Example: Tanks r 0 () h 1 () r 1 () h 2 () r 2 () r 0 () r 2 () ank
72 Example: Cell Phone Sysem sound ou sound in sound in cell phone sound ou
73 Example: Cell Phone Sysem sound ou sound in sound in sound ou cell phone
74 Signals and Sysems: Uniform Represenaions x() y() mass & spring r0() h1() r0() r2() r1() ank h2() r2() sound ou sound in sound ou sound in cell phone elecrical, mechanical, chemical, opical, acousic, biological, financial,...
75 Signals and Sysems: Uniformiy Modulariy sound ou sound in sound in cell phone E/M ower opic fiber ower E/M cell phone sound ou focus on he flow of informaion absrac away everyhing else
76 Signals and Sysems: Broad Applicabiliy mechanics circuis medical v i A R 1 v o R 2 signal in signal ou
77 Discree-Time Sysems
78 Example: Bank accoun Transacions (deposis/wihdrawals) recorded daily (DT) Deposis are an inpu (of money) ino he. How are wihdrawals represened in he framework of signals and s? 1. as an inpu signal 2. as an oupu signal 3. none of he above
79 Example: Bank Accoun Transacions (deposis/wihdrawals) recorded daily (DT) x[n] y[n] n accoun $0.00 n $ deposied oday curren balance
80 Example: Bank Accoun Transacions (deposis/wihdrawals) recorded daily (DT) x[n] y[n] n accoun $1.00 n $ deposied oday curren balance
81 Example: Bank Accoun Transacions (deposis/wihdrawals) recorded daily (DT) x[n] y[n] n accoun $1.00 n $ deposied oday curren balance
82 Example: Bank Accoun Transacions (deposis/wihdrawals) recorded daily (DT) x[n] y[n] n accoun $2.00 n $ deposied oday curren balance
83 Example: Bank Accoun Transacions (deposis/wihdrawals) recorded daily (DT) x[n] y[n] n accoun $3.00 n $ deposied oday curren balance
84 Example: Bank Accoun Transacions (deposis/wihdrawals) recorded daily (DT) x[n] y[n] n accoun $5.00 n $ deposied oday curren balance
85 Example: Bank Accoun Transacions (deposis/wihdrawals) recorded daily (DT) x[n] y[n] n accoun $6.00 n $ deposied oday curren balance
86 Example: Bank Accoun Transacions (deposis/wihdrawals) recorded daily (DT) x[n] y[n] n accoun $7.00 n $ deposied oday curren balance
87 Example: Bank Accoun Wihdrawals are negaive deposis./ x[n] y[n] n accoun $0.00 n $ deposied oday curren balance
88 Example: Bank Accoun Wihdrawals are negaive deposis./ x[n] y[n] n accoun $1.00 n $ deposied oday curren balance
89 Example: Bank Accoun Wihdrawals are negaive deposis./ x[n] y[n] n accoun $2.00 n $ deposied oday curren balance
90 Example: Bank Accoun Wihdrawals are negaive deposis./ x[n] y[n] n accoun $1.00 n $ deposied oday curren balance
91 Example: Bank Accoun Wihdrawals are negaive deposis./ x[n] y[n] n accoun $3.00 n $ deposied oday curren balance
92 Example: Bank Accoun Wihdrawals are negaive deposis./ x[n] y[n] n accoun $2.00 n $ deposied oday curren balance
93 Example: Bank Accoun Wihdrawals are negaive deposis./ x[n] y[n] n accoun $1.00 n $ deposied oday curren balance
94 Example: Bank Accoun Wihdrawals are negaive deposis./ x[n] y[n] n accoun $1.00 n $ deposied oday curren balance
95 Example: Bank Accoun Compound ineres./ x[n] y[n] n accoun $1.00 n $ deposied oday curren balance
96 Example: Bank Accoun Compound ineres./ x[n] y[n] n accoun $1.05 n $ deposied oday curren balance
97 Example: Bank Accoun Compound ineres./ x[n] y[n] n accoun $1.10 n $ deposied oday curren balance
98 Example: Bank Accoun Compound ineres./ x[n] y[n] n accoun $1.16 n $ deposied oday curren balance
99 Example: Bank Accoun Compound ineres./ x[n] y[n] n accoun $1.22 n $ deposied oday curren balance
100 Example: Bank Accoun Compound ineres./ x[n] y[n] n accoun $1.28 n $ deposied oday curren balance
101 Example: Bank Accoun Compound ineres./ x[n] y[n] n accoun $2.34 n $ deposied oday curren balance
102 Example: Bank Accoun Compound ineres./ x[n] y[n] n accoun $1.41 n $ deposied oday curren balance
103 Example: Bank Accoun Early Reiremen? How soon can you reire if living expenses: $25,000 per year rae of savings: $10,000 per year 5% annual ineres live off your savings ill age 80? x[n] n y[n] n save reire
104 Populaion Growh
105 Populaion Growh
106 Populaion Growh
107 Populaion Growh
108 Populaion Growh
109 Populaion Growh
110 Populaion Growh
111 Populaion Growh
112 Populaion Growh
113 Populaion Growh How does he number of pairs of rabbis grow? 1. logarihmic ( f [n] = O(log n)) 2. polynomial ( f [n] = O(n k ) for some k) 3. exponenial ( f [n] = O(z n ) for some z)
6.003 Homework 1. Problems. Due at the beginning of recitation on Wednesday, February 10, 2010.
6.003 Homework Due a he beginning of reciaion on Wednesday, February 0, 200. Problems. Independen and Dependen Variables Assume ha he heigh of a waer wave is given by g(x v) where x is disance, v is velociy,
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signals & Sysems Prof. Mark Fowler Noe Se #1 C-T Sysems: Convoluion Represenaion Reading Assignmen: Secion 2.6 of Kamen and Heck 1/11 Course Flow Diagram The arrows here show concepual flow beween
Lecture 1 Overview. course mechanics. outline & topics. what is a linear dynamical system? why study linear systems? some examples
EE263 Auumn 27-8 Sephen Boyd Lecure 1 Overview course mechanics ouline & opics wha is a linear dynamical sysem? why sudy linear sysems? some examples 1 1 Course mechanics all class info, lecures, homeworks,
6.01: Introduction to EECS I Lecture 8 March 29, 2011
6.01: Inroducion o EES I Lecure 8 March 29, 2011 6.01: Inroducion o EES I Op-Amps Las Time: The ircui Absracion ircuis represen sysems as connecions of elemens hrough which currens (hrough variables) flow
CSE 3802 / ECE Numerical Methods in Scientific Computation. Jinbo Bi. Department of Computer Science & Engineering
CSE 3802 / ECE 3431 Numerical Mehods in Scienific Compuaion Jinbo Bi Deparmen of Compuer Science & Engineering hp://www.engr.uconn.edu/~jinbo 1 Ph.D in Mahemaics The Insrucor Previous professional experience:
EECS 2602 Winter Laboratory 3 Fourier series, Fourier transform and Bode Plots in MATLAB
EECS 6 Winer 7 Laboraory 3 Fourier series, Fourier ransform and Bode Plos in MATLAB Inroducion: The objecives of his lab are o use MATLAB:. To plo periodic signals wih Fourier series represenaion. To obain
6.003: Signal Processing
6.003: Signal Processing Working wih Signals Overview of Subjec Signals: Definiions, Examples, and Operaions Basis Funcions and Transforms Sepember 6, 2018 Welcome o 6.003 Piloing a new version of 6.003
( ) ( ) if t = t. It must satisfy the identity. So, bulkiness of the unit impulse (hyper)function is equal to 1. The defining characteristic is
UNIT IMPULSE RESPONSE, UNIT STEP RESPONSE, STABILITY. Uni impulse funcion (Dirac dela funcion, dela funcion) rigorously defined is no sricly a funcion, bu disribuion (or measure), precise reamen requires
KEEE313(03) Signals and Systems. Chang-Su Kim
KEEE313(03) Signals and Sysems Chang-Su Kim Course Informaion Course homepage hp://mcl.korea.ac.kr Lecurer Chang-Su Kim Office: Engineering Bldg, Rm 508 E-mail: changsukim@korea.ac.kr Tuor 허육 (yukheo@mcl.korea.ac.kr)
LAPLACE TRANSFORM AND TRANSFER FUNCTION
CHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION Professor Dae Ryook Yang Spring 2018 Dep. of Chemical and Biological Engineering 5-1 Road Map of he Lecure V Laplace Transform and Transfer funcions
6.003: Signals and Systems. Relations among Fourier Representations
6.003: Signals and Sysems Relaions among Fourier Represenaions April 22, 200 Mid-erm Examinaion #3 W ednesday, April 28, 7:30-9:30pm. No reciaions on he day of he exam. Coverage: Lecures 20 Reciaions 20
6.003: Signals and Systems
6.003: Signals and Sysems Relaions among Fourier Represenaions November 5, 20 Mid-erm Examinaion #3 Wednesday, November 6, 7:30-9:30pm, No reciaions on he day of he exam. Coverage: Lecures 8 Reciaions
Continuous Time Linear Time Invariant (LTI) Systems. Dr. Ali Hussein Muqaibel. Introduction
/9/ Coninuous Time Linear Time Invarian (LTI) Sysems Why LTI? Inroducion Many physical sysems. Easy o solve mahemaically Available informaion abou analysis and design. We can apply superposiion LTI Sysem
Chapter 1 Fundamental Concepts
Chaper 1 Fundamenal Conceps 1 Signals A signal is a paern of variaion of a physical quaniy, ofen as a funcion of ime (bu also space, disance, posiion, ec). These quaniies are usually he independen variables
Lecture Notes 3: Quantitative Analysis in DSGE Models: New Keynesian Model
Lecure Noes 3: Quaniaive Analysis in DSGE Models: New Keynesian Model Zhiwei Xu, Email: xuzhiwei@sju.edu.cn The moneary policy plays lile role in he basic moneary model wihou price sickiness. We now urn
Chapter 7 Response of First-order RL and RC Circuits
Chaper 7 Response of Firs-order RL and RC Circuis 7.- The Naural Response of RL and RC Circuis 7.3 The Sep Response of RL and RC Circuis 7.4 A General Soluion for Sep and Naural Responses 7.5 Sequenial
CHAPTER 2 Signals And Spectra
CHAPER Signals And Specra Properies of Signals and Noise In communicaion sysems he received waveform is usually caegorized ino he desired par conaining he informaion, and he undesired par. he desired par
MATH ANALYSIS HONORS UNIT 6 EXPONENTIAL FUNCTIONS TOTAL NAME DATE PERIOD DATE TOPIC ASSIGNMENT /19 10/22 10/23 10/24 10/25 10/26 10/29 10/30
NAME DATE PERIOD MATH ANALYSIS HONORS UNIT 6 EXPONENTIAL FUNCTIONS DATE TOPIC ASSIGNMENT 10 0 10/19 10/ 10/ 10/4 10/5 10/6 10/9 10/0 10/1 11/1 11/ TOTAL Mah Analysis Honors Workshee 1 Eponenial Funcions
University of Cyprus Biomedical Imaging and Applied Optics. Appendix. DC Circuits Capacitors and Inductors AC Circuits Operational Amplifiers
Universiy of Cyprus Biomedical Imaging and Applied Opics Appendix DC Circuis Capaciors and Inducors AC Circuis Operaional Amplifiers Circui Elemens An elecrical circui consiss of circui elemens such as
To become more mathematically correct, Circuit equations are Algebraic Differential equations. from KVL, KCL from the constitutive relationship
Laplace Tranform (Lin & DeCarlo: Ch 3) ENSC30 Elecric Circui II The Laplace ranform i an inegral ranformaion. I ranform: f ( ) F( ) ime variable complex variable From Euler > Lagrange > Laplace. Hence,
F.LE.A.4: Exponential Growth
Regens Exam Quesions F.LE.A.4: Exponenial Growh www.jmap.org Name: F.LE.A.4: Exponenial Growh 1 A populaion of rabbis doubles every days according o he formula P = 10(2), where P is he populaion of rabbis
Simulation-Solving Dynamic Models ABE 5646 Week 2, Spring 2010
Simulaion-Solving Dynamic Models ABE 5646 Week 2, Spring 2010 Week Descripion Reading Maerial 2 Compuer Simulaion of Dynamic Models Finie Difference, coninuous saes, discree ime Simple Mehods Euler Trapezoid
Q1) [20 points] answer for the following questions (ON THIS SHEET):
![Q1) [20 points] answer for the following questions (ON THIS SHEET):](/thumbs/87/96063197.jpg "Q1) [20 points] answer for the following questions (ON THIS SHEET):")
Dr. Anas Al Tarabsheh The Hashemie Universiy Elecrical and Compuer Engineering Deparmen (Makeup Exam) Signals and Sysems Firs Semeser 011/01 Final Exam Dae: 1/06/01 Exam Duraion: hours Noe: means convoluion
MEMS 0031 Electric Circuits
MEMS 0031 Elecric Circuis Chaper 1 Circui variables Chaper/Lecure Learning Objecives A he end of his lecure and chaper, you should able o: Represen he curren and volage of an elecric circui elemen, paying
4.1 - Logarithms and Their Properties
Chaper 4 Logarihmic Funcions 4.1 - Logarihms and Their Properies Wha is a Logarihm? We define he common logarihm funcion, simply he log funcion, wrien log 10 x log x, as follows: If x is a posiive number,
STATE-SPACE MODELLING. A mass balance across the tank gives:
B. Lennox and N.F. Thornhill, 9, Sae Space Modelling, IChemE Process Managemen and Conrol Subjec Group Newsleer STE-SPACE MODELLING Inroducion: Over he pas decade or so here has been an ever increasing
Essential Microeconomics : OPTIMAL CONTROL 1. Consider the following class of optimization problems
Essenial Microeconomics -- 6.5: OPIMAL CONROL Consider he following class of opimizaion problems Max{ U( k, x) + U+ ( k+ ) k+ k F( k, x)}. { x, k+ } = In he language of conrol heory, he vecor k is he vecor
Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:
Serial : 0. ND_NW_EE_Signal & Sysems_4068 Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkaa Pana Web: E-mail: info@madeeasy.in Ph: 0-4546 CLASS TEST 08-9 ELECTRICAL ENGINEERING
8. Basic RL and RC Circuits
8. Basic L and C Circuis This chaper deals wih he soluions of he responses of L and C circuis The analysis of C and L circuis leads o a linear differenial equaion This chaper covers he following opics
R =, C = 1, and f ( t ) = 1 for 1 second from t = 0 to t = 1. The initial charge on the capacitor is q (0) = 0. We have already solved this problem.
Theoreical Physics Prof. Ruiz, UNC Asheville, docorphys on YouTube Chaper U Noes. Green's Funcions R, C 1, and f ( ) 1 for 1 second from o 1. The iniial charge on he capacior is q (). We have already solved
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 3 Signals & Sysems Prof. Mark Fowler Noe Se #2 Wha are Coninuous-Time Signals??? Reading Assignmen: Secion. of Kamen and Heck /22 Course Flow Diagram The arrows here show concepual flow beween ideas.
Laplace Transform and its Relation to Fourier Transform
Chaper 6 Laplace Transform and is Relaion o Fourier Transform (A Brief Summary) Gis of he Maer 2 Domains of Represenaion Represenaion of signals and sysems Time Domain Coninuous Discree Time Time () [n]
Signal and System (Chapter 3. Continuous-Time Systems)
Signal and Sysem (Chaper 3. Coninuous-Time Sysems) Prof. Kwang-Chun Ho kwangho@hansung.ac.kr Tel: 0-760-453 Fax:0-760-4435 1 Dep. Elecronics and Informaion Eng. 1 Nodes, Branches, Loops A nework wih b
From Complex Fourier Series to Fourier Transforms
Topic From Complex Fourier Series o Fourier Transforms. Inroducion In he previous lecure you saw ha complex Fourier Series and is coeciens were dened by as f ( = n= C ne in! where C n = T T = T = f (e
EE 224 Signals and Systems I Complex numbers sinusodal signals Complex exponentials e jωt phasor addition
EE 224 Signals and Sysems I Complex numbers sinusodal signals Complex exponenials e jω phasor addiion 1/28 Complex Numbers Recangular Polar y z r z θ x Good for addiion/subracion Good for muliplicaion/division
Reading from Young & Freedman: For this topic, read sections 25.4 & 25.5, the introduction to chapter 26 and sections 26.1 to 26.2 & 26.4.
PHY1 Elecriciy Topic 7 (Lecures 1 & 11) Elecric Circuis n his opic, we will cover: 1) Elecromoive Force (EMF) ) Series and parallel resisor combinaions 3) Kirchhoff s rules for circuis 4) Time dependence
CONTROL SYSTEMS, ROBOTICS AND AUTOMATION Vol. XI Control of Stochastic Systems - P.R. Kumar
CONROL OF SOCHASIC SYSEMS P.R. Kumar Deparmen of Elecrical and Compuer Engineering, and Coordinaed Science Laboraory, Universiy of Illinois, Urbana-Champaign, USA. Keywords: Markov chains, ransiion probabiliies,
APPM 2360 Homework Solutions, Due June 10
2.2.2: Find general soluions for he equaion APPM 2360 Homework Soluions, Due June 10 Soluion: Finding he inegraing facor, dy + 2y = 3e µ) = e 2) = e 2 Muliplying he differenial equaion by he inegraing
CHBE320 LECTURE IV MATHEMATICAL MODELING OF CHEMICAL PROCESS. Professor Dae Ryook Yang
CHBE320 LECTURE IV MATHEMATICAL MODELING OF CHEMICAL PROCESS Professor Dae Ryook Yang Spring 208 Dep. of Chemical and Biological Engineering CHBE320 Process Dynamics and Conrol 4- Road Map of he Lecure
04. Kinetics of a second order reaction
4. Kineics of a second order reacion Imporan conceps Reacion rae, reacion exen, reacion rae equaion, order of a reacion, firs-order reacions, second-order reacions, differenial and inegraed rae laws, Arrhenius
Section 7.4 Modeling Changing Amplitude and Midline
488 Chaper 7 Secion 7.4 Modeling Changing Ampliude and Midline While sinusoidal funcions can model a variey of behaviors, i is ofen necessary o combine sinusoidal funcions wih linear and exponenial curves
Notes 8B Day 1 Doubling Time
Noes 8B Day 1 Doubling ime Exponenial growh leads o repeaed doublings (see Graph in Noes 8A) and exponenial decay leads o repeaed halvings. In his uni we ll be convering beween growh (or decay) raes and
Lecture #6: Continuous-Time Signals
EEL5: Discree-Time Signals and Sysems Lecure #6: Coninuous-Time Signals Lecure #6: Coninuous-Time Signals. Inroducion In his lecure, we discussed he ollowing opics:. Mahemaical represenaion and ransormaions
RC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
Signals and Systems Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin
EE 345S Real-Time Digial Signal Processing Lab Spring 26 Signals and Sysems Prof. Brian L. Evans Dep. of Elecrical and Compuer Engineering The Universiy of Texas a Ausin Review Signals As Funcions of Time
Basic Circuit Elements Professor J R Lucas November 2001
Basic Circui Elemens - J ucas An elecrical circui is an inerconnecion of circui elemens. These circui elemens can be caegorised ino wo ypes, namely acive and passive elemens. Some Definiions/explanaions
Math 333 Problem Set #2 Solution 14 February 2003
Mah 333 Problem Se #2 Soluion 14 February 2003 A1. Solve he iniial value problem dy dx = x2 + e 3x ; 2y 4 y(0) = 1. Soluion: This is separable; we wrie 2y 4 dy = x 2 + e x dx and inegrae o ge The iniial
Continuous Time. Time-Domain System Analysis. Impulse Response. Impulse Response. Impulse Response. Impulse Response. ( t) + b 0.
Time-Domain Sysem Analysis Coninuous Time. J. Robers - All Righs Reserved. Edied by Dr. Rober Akl 1. J. Robers - All Righs Reserved. Edied by Dr. Rober Akl 2 Le a sysem be described by a 2 y ( ) + a 1
PHYS 100: Lecture 2. Motion at Constant Acceleration. Relative Motion: Reference Frames. x x = v t + a t. x = vdt. v = adt. x Tortoise.
a PHYS 100: Lecure 2 Moion a Consan Acceleraion a 0 0 Area a 0 a 0 v ad v v0 a0 v 0 x vd 0 A(1/2)( v) Area v 0 v v-v 0 v 0 x x v + a 1 0 0 2 0 2 Relaive Moion: Reference Frames x d Achilles Toroise x Toroise
Learning Enhancement Team
Learning Enhancemen Team Model answers: Exponenial Funcions Exponenial Funcions sudy guide 1 i) The base rae of growh b is equal o 3 You can see his by noicing ha 1b 36 in his sysem, dividing boh sides
3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon
3..3 INRODUCION O DYNAMIC OPIMIZAION: DISCREE IME PROBLEMS A. he Hamilonian and Firs-Order Condiions in a Finie ime Horizon Define a new funcion, he Hamilonian funcion, H. H he change in he oal value of
4.1 INTRODUCTION TO THE FAMILY OF EXPONENTIAL FUNCTIONS
Funcions Modeling Change: A Preparaion for Calculus, 4h Ediion, 2011, Connally 4.1 INTRODUCTION TO THE FAMILY OF EXPONENTIAL FUNCTIONS Growing a a Consan Percen Rae Example 2 During he 2000 s, he populaion
not to be republished NCERT MATHEMATICAL MODELLING Appendix 2 A.2.1 Introduction A.2.2 Why Mathematical Modelling?
256 MATHEMATICS A.2.1 Inroducion In class XI, we have learn abou mahemaical modelling as an aemp o sudy some par (or form) of some real-life problems in mahemaical erms, i.e., he conversion of a physical
Chapter 3: Signal Transmission and Filtering. A. Bruce Carlson Paul B. Crilly 2010 The McGraw-Hill Companies
Communicaion Sysems, 5e Chaper 3: Signal Transmission and Filering A. Bruce Carlson Paul B. Crilly 00 The McGraw-Hill Companies Chaper 3: Signal Transmission and Filering Response of LTI sysems Signal
INDEX. Transient analysis 1 Initial Conditions 1
INDEX Secion Page Transien analysis 1 Iniial Condiions 1 Please inform me of your opinion of he relaive emphasis of he review maerial by simply making commens on his page and sending i o me a: Frank Mera
Vehicle Arrival Models : Headway
Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where
Welcome Back to Physics 215!
Welcome Back o Physics 215! (General Physics I) Thurs. Jan 19 h, 2017 Lecure01-2 1 Las ime: Syllabus Unis and dimensional analysis Today: Displacemen, velociy, acceleraion graphs Nex ime: More acceleraion
1 Differential Equation Investigations using Customizable
Differenial Equaion Invesigaions using Cusomizable Mahles Rober Decker The Universiy of Harford Absrac. The auhor has developed some plaform independen, freely available, ineracive programs (mahles) for
A Note on the Equivalence of Fractional Relaxation Equations to Differential Equations with Varying Coefficients
mahemaics Aricle A Noe on he Equivalence of Fracional Relaxaion Equaions o Differenial Equaions wih Varying Coefficiens Francesco Mainardi Deparmen of Physics and Asronomy, Universiy of Bologna, and he
RL Lecture 7: Eligibility Traces. R. S. Sutton and A. G. Barto: Reinforcement Learning: An Introduction 1
RL Lecure 7: Eligibiliy Traces R. S. Suon and A. G. Baro: Reinforcemen Learning: An Inroducion 1 N-sep TD Predicion Idea: Look farher ino he fuure when you do TD backup (1, 2, 3,, n seps) R. S. Suon and
Lecture Outline. Introduction Transmission Line Equations Transmission Line Wave Equations 8/10/2018. EE 4347 Applied Electromagnetics.
8/10/018 Course Insrucor Dr. Raymond C. Rumpf Office: A 337 Phone: (915) 747 6958 E Mail: rcrumpf@uep.edu EE 4347 Applied Elecromagneics Topic 4a Transmission Line Equaions Transmission These Line noes
R.#W.#Erickson# Department#of#Electrical,#Computer,#and#Energy#Engineering# University#of#Colorado,#Boulder#
.#W.#Erickson# Deparmen#of#Elecrical,#Compuer,#and#Energy#Engineering# Universiy#of#Colorado,#Boulder# Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance,
6.003: Signal Processing
6.003: Signal Processing Coninuous-Time Fourier Transform Definiion Examples Properies Relaion o Fourier Series Sepember 5, 08 Quiz Thursday, Ocober 4, from 3pm o 5pm. No lecure on Ocober 4. The exam is
Learning Objectives: Practice designing and simulating digital circuits including flip flops Experience state machine design procedure
Lab 4: Synchronous Sae Machine Design Summary: Design and implemen synchronous sae machine circuis and es hem wih simulaions in Cadence Viruoso. Learning Objecives: Pracice designing and simulaing digial
Lectures 29 and 30 BIQUADRATICS AND STATE SPACE OP AMP REALIZATIONS. I. Introduction
EE-202/445, 3/18/18 9-1 R. A. DeCarlo Lecures 29 and 30 BIQUADRATICS AND STATE SPACE OP AMP REALIZATIONS I. Inroducion 1. The biquadraic ransfer funcion has boh a 2nd order numeraor and a 2nd order denominaor:
ADVANCED MATHEMATICS FOR ECONOMICS /2013 Sheet 3: Di erential equations
ADVANCED MATHEMATICS FOR ECONOMICS - /3 Shee 3: Di erenial equaions Check ha x() =± p ln(c( + )), where C is a posiive consan, is soluion of he ODE x () = Solve he following di erenial equaions: (a) x
KEY. Math 334 Midterm III Winter 2008 section 002 Instructor: Scott Glasgow
KEY Mah 334 Miderm III Winer 008 secion 00 Insrucor: Sco Glasgow Please do NOT wrie on his exam. No credi will be given for such work. Raher wrie in a blue book, or on your own paper, preferably engineering
Linear Time-invariant systems, Convolution, and Cross-correlation
Linear Time-invarian sysems, Convoluion, and Cross-correlaion (1) Linear Time-invarian (LTI) sysem A sysem akes in an inpu funcion and reurns an oupu funcion. x() T y() Inpu Sysem Oupu y() = T[x()] An
Math Week 14 April 16-20: sections first order systems of linear differential equations; 7.4 mass-spring systems.
Mah 2250-004 Week 4 April 6-20 secions 7.-7.3 firs order sysems of linear differenial equaions; 7.4 mass-spring sysems. Mon Apr 6 7.-7.2 Sysems of differenial equaions (7.), and he vecor Calculus we need
Designing Information Devices and Systems I Spring 2019 Lecture Notes Note 17
EES 16A Designing Informaion Devices and Sysems I Spring 019 Lecure Noes Noe 17 17.1 apaciive ouchscreen In he las noe, we saw ha a capacior consiss of wo pieces on conducive maerial separaed by a nonconducive
5. Response of Linear Time-Invariant Systems to Random Inputs
Sysem: 5. Response of inear ime-invarian Sysems o Random Inpus 5.. Discree-ime linear ime-invarian (IV) sysems 5... Discree-ime IV sysem IV sysem xn ( ) yn ( ) [ xn ( )] Inpu Signal Sysem S Oupu Signal
Cash Flow Valuation Mode Lin Discrete Time
IOSR Journal of Mahemaics (IOSR-JM) e-issn: 2278-5728,p-ISSN: 2319-765X, 6, Issue 6 (May. - Jun. 2013), PP 35-41 Cash Flow Valuaion Mode Lin Discree Time Olayiwola. M. A. and Oni, N. O. Deparmen of Mahemaics
Mon Apr 9 EP 7.6 Convolutions and Laplace transforms. Announcements: Warm-up Exercise:
Mah 225-4 Week 3 April 9-3 EP 7.6 - convoluions; 6.-6.2 - eigenvalues, eigenvecors and diagonalizabiliy; 7. - sysems of differenial equaions. Mon Apr 9 EP 7.6 Convoluions and Laplace ransforms. Announcemens:
System Processes input signal (excitation) and produces output signal (response)
Signal A funcion of ime Sysem Processes inpu signal (exciaion) and produces oupu signal (response) Exciaion Inpu Sysem Oupu Response 1. Types of signals 2. Going from analog o digial world 3. An example
ACCUMULATION. Section 7.5 Calculus AP/Dual, Revised /26/2018 7:27 PM 7.5A: Accumulation 1
ACCUMULATION Secion 7.5 Calculus AP/Dual, Revised 2019 vie.dang@humbleisd.ne 12/26/2018 7:27 PM 7.5A: Accumulaion 1 APPLICATION PROBLEMS A. Undersand he quesion. I is ofen no necessary o as much compuaion
Exam 1 Solutions. 1 Question 1. February 10, Part (A) 1.2 Part (B) To find equilibrium solutions, set P (t) = C = dp
Exam Soluions Februar 0, 05 Quesion. Par (A) To find equilibrium soluions, se P () = C = = 0. This implies: = P ( P ) P = P P P = P P = P ( + P ) = 0 The equilibrium soluion are hus P () = 0 and P () =..
Section 4.4 Logarithmic Properties
Secion. Logarihmic Properies 5 Secion. Logarihmic Properies In he previous secion, we derived wo imporan properies of arihms, which allowed us o solve some asic eponenial and arihmic equaions. Properies
ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 6 SECTION 6.1: LIFE CYCLE CONSUMPTION AND WEALTH T 1. . Let ct. ) is a strictly concave function of c
John Riley December 00 S O EVEN NUMBERED EXERCISES IN CHAPER 6 SECION 6: LIFE CYCLE CONSUMPION AND WEALH Eercise 6-: Opimal saving wih more han one commodiy A consumer has a period uiliy funcion δ u (
Solutions to Assignment 1
MA 2326 Differenial Equaions Insrucor: Peronela Radu Friday, February 8, 203 Soluions o Assignmen. Find he general soluions of he following ODEs: (a) 2 x = an x Soluion: I is a separable equaion as we
Lecture #8 Redfield theory of NMR relaxation
Lecure #8 Redfield heory of NMR relaxaion Topics The ineracion frame of reference Perurbaion heory The Maser Equaion Handous and Reading assignmens van de Ven, Chapers 6.2. Kowalewski, Chaper 4. Abragam
4/9/2012. Signals and Systems KX5BQY EE235. Today s menu. System properties
Signals and Sysems hp://www.youube.com/v/iv6fo KX5BQY EE35 oday s menu Good weeend? Sysem properies iy Superposiion! Sysem properies iy: A Sysem is if i mees he following wo crieria: If { x( )} y( ) and
Chapter 7: Inverse-Response Systems
Chaper 7: Invere-Repone Syem Normal Syem Invere-Repone Syem Baic Sar ou in he wrong direcion End up in he original eady-ae gain value Two or more yem wih differen magniude and cale in parallel Main yem
Week Exp Date Lecture topic(s) Assignment. Course Overview. Intro: Measurements, uncertainties. Lab: Discussion of Exp 3 goals, setup
Schedule for Physics BL - Fall 01 Find relevan Lab Guides on he course web sie o prepare for Quizzes. Reading maerial and pracice problems are from Taylor, Error Analysis. Week Exp Dae Lecure opic(s) Assignmen
MA 366 Review - Test # 1
MA 366 Review - Tes # 1 Fall 5 () Resuls from Calculus: differeniaion formulas, implici differeniaion, Chain Rule; inegraion formulas, inegraion b pars, parial fracions, oher inegraion echniques. (1) Order
8.022 (E&M) Lecture 16
8. (E&M) ecure 16 Topics: Inducors in circuis circuis circuis circuis as ime Our second lecure on elecromagneic inducance 3 ways of creaing emf using Faraday s law: hange area of circui S() hange angle
Time Domain Transfer Function of the Induction Motor
Sudies in Engineering and Technology Vol., No. ; Augus 0 ISSN 008 EISSN 006 Published by Redfame Publishing URL: hp://se.redfame.com Time Domain Transfer Funcion of he Inducion Moor N N arsoum Correspondence:
Outline Chapter 2: Signals and Systems
Ouline Chaper 2: Signals and Sysems Signals Basics abou Signal Descripion Fourier Transform Harmonic Decomposiion of Periodic Waveforms (Fourier Analysis) Definiion and Properies of Fourier Transform Imporan
2.4 Cuk converter example
2.4 Cuk converer example C 1 Cuk converer, wih ideal swich i 1 i v 1 2 1 2 C 2 v 2 Cuk converer: pracical realizaion using MOSFET and diode C 1 i 1 i v 1 2 Q 1 D 1 C 2 v 2 28 Analysis sraegy This converer
28. Narrowband Noise Representation
Narrowband Noise Represenaion on Mac 8. Narrowband Noise Represenaion In mos communicaion sysems, we are ofen dealing wih band-pass filering of signals. Wideband noise will be shaped ino bandlimied noise.
Matlab and Python programming: how to get started
Malab and Pyhon programming: how o ge sared Equipping readers he skills o wrie programs o explore complex sysems and discover ineresing paerns from big daa is one of he main goals of his book. In his chaper,
2.160 System Identification, Estimation, and Learning. Lecture Notes No. 8. March 6, 2006
2.160 Sysem Idenificaion, Esimaion, and Learning Lecure Noes No. 8 March 6, 2006 4.9 Eended Kalman Filer In many pracical problems, he process dynamics are nonlinear. w Process Dynamics v y u Model (Linearized)
Laplace Transforms. Examples. Is this equation differential? y 2 2y + 1 = 0, y 2 2y + 1 = 0, (y ) 2 2y + 1 = cos x,
Laplace Transforms Definiion. An ordinary differenial equaion is an equaion ha conains one or several derivaives of an unknown funcion which we call y and which we wan o deermine from he equaion. The equaion
Representing a Signal. Continuous-Time Fourier Methods. Linearity and Superposition. Real and Complex Sinusoids. Jean Baptiste Joseph Fourier
Represening a Signal Coninuous-ime ourier Mehods he convoluion mehod for finding he response of a sysem o an exciaion aes advanage of he lineariy and imeinvariance of he sysem and represens he exciaion
5.1 - Logarithms and Their Properties
Chaper 5 Logarihmic Funcions 5.1 - Logarihms and Their Properies Suppose ha a populaion grows according o he formula P 10, where P is he colony size a ime, in hours. When will he populaion be 2500? We
cs/ee 143 Communication Networks Steven Low CMS, EE, Caltech Fall 2012
cs/ee 143 Communicaion Neworks Seven Low CMS, EE, Calech Fall 2012 Inroducion o Communicaion Neworks Seven Low Calech, Zhejiang Universiy Course ouline 1. Basic proocols and projecs n 1 s hree weeks of
6.2 Transforms of Derivatives and Integrals.
SEC. 6.2 Transforms of Derivaives and Inegrals. ODEs 2 3 33 39 23. Change of scale. If l( f ()) F(s) and c is any 33 45 APPLICATION OF s-shifting posiive consan, show ha l( f (c)) F(s>c)>c (Hin: In Probs.
Sterilization D Values
Seriliaion D Values Seriliaion by seam consis of he simple observaion ha baceria die over ime during exposure o hea. They do no all live for a finie period of hea exposure and hen suddenly die a once,
Hint: There's a table of particular solutions at the end of today's notes.
Mah 8- Fri Apr 4, Finish Wednesday's noes firs Then 94 Forced oscillaion problems via Fourier Series Today we will revisi he forced oscillaion problems of las Friday, where we prediced wheher or no resonance
Linear Response Theory: The connection between QFT and experiments
Phys540.nb 39 3 Linear Response Theory: The connecion beween QFT and experimens 3.1. Basic conceps and ideas Q: How do we measure he conduciviy of a meal? A: we firs inroduce a weak elecric field E, and
Chemical Engineering Thermodynamics
Engi-3434 Chemical Engineering Thermodynamics Dr. Charles Xu @ Chemical Engineering, Lakehead Universiy Chemical Engineering Thermodynamics Insrucor: Dr. Charles Xu, P.Eng. Associae Professor Deparmen