Chapter 8: Response of Linear Systems to Random Inputs
|
|
|
- Osborn Atkinson
- 6 years ago
- Views:
Transcription
1 Caper 8: epone of Linear yem o anom Inpu 8- Inroucion 8- nalyi in e ime Domain 8- Mean an Variance Value of yem Oupu 8-4 uocorrelaion Funcion of yem Oupu 8-5 Crocorrelaion beeen Inpu an Oupu 8-6 ample of ime-domain yem nalyi 8-7 nalyi in e Frequency Domain 8-8 pecral Deniy a e yem Oupu 8-9 Cro-pecral Deniie beeen Inpu an Oupu 8- ample of Frequency-Domain nalyi 8- umerical Compuaion of yem Oupu Concep: Linear yem nalyi in e ime Domain Mean an Variance Value of yem Oupu uocorrelaion Funcion of yem Oupu Crocorrelaion beeen Inpu an Oupu ample of ime-domain yem nalyi nalyi in e Frequency Domain pecral Deniy a e yem Oupu Frequency Limie Filering Banlimie Wie oie IMO yem Cro-pecral Deniie beeen Inpu an Oupu ample of Frequency-Domain nalyi umerical Compuaion of yem Oupu imulaing ocaic yem epone oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 of 6 C 8
2 Caper 8: epone of Linear yem o anom Inpu Linear ranformaion of ignal: convoluion in e ime omain y yem y Linear ranformaion of ignal: muliplicaion in e Laplace omain e convoluion Inegral (applying a caual filer) y or y Commen: Dr. Bazuin ill ue caual filer, efine a,, an en oing o ypically prefer oing convoluion a y oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 of 6 C 8
3 more realiic yem D G C G P P C e Proce mu be oberve an conrolle. anom noie, inerference, or iurbance are preen in all inpu o e yem an meauremen of e oupu of e yem. e elecronic conrol mu eermine a i imporan an a in an conrol e yem in orer o operae i properly. We ue filer o eliminae noie in frequency ban no of inere. We ue correlaion an opimal ignal eecor o look for knon paern epece in e ignal. We ue a-priori informaion o eign e yem for all knon. We can collece aiic in e form of auo an cro-covariance o eermine curren operaion. Bae on operaing parameer e mu make eciion an ac upon em. oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 of 6 C 8
4 oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 4 of 6 C 8 e Mean Value a a yem Oupu fer efining e convoluion, e can ue e epece value operaor noe a proceing of Wie-ene aionary anom Procee i eire an uually implie. For a ie-ene aionary proce, i reul in e mean of e oupu i e mean of e inpu ime e coeren gain of e filer. e coeren gain of a filer i efine a: gain erefore, gain e Mean quare Value a a yem Oupu erefore, ake e convoluion of e auocorrelaion funcion an en um e filer-eige reul from o infiniy.
5 oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 5 of 6 C 8 e uocorrelaion a a yem Oupu e epece value of e prouc of o iinc convoluion: Ienifying an forming e inpu auocorrelaion or oice a fir, you convolve e inpu auocorrelaion funcion i e filer funcion an en you convolve e reul i a ime invere verion of e filer!
6 oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 6 of 6 C 8 e Poer pecral Deniy a a yem Oupu e poer pecral eniy i e Fourier ranform of e auocorrelaion: i ep i ep Were y For a W, ergoic proce, i i ere e ave goen before. o e nee o perform e Fourier ranform o fin e PD! i ep
7 aking e Poer pecral Deniy ep i Iolaing e ranform o funcion in ime (au) ep i ep j eparaing epenen an inepenen elemen bae on e inegraion ep ep j j j ep erefore j ep or elaion of pecral Deniy o e Crocorrelaion Funcion you mig epec, compuaion of e cro-pecral only a a ingle filer PD erm. an an oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 7 of 6 C 8
8 oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 8 of 6 C ample of ime-domain nalyi: I i imporan o remember bo e ime omain an frequency omain relaionip in orer o pick e one a i eaier bae on e ignal ype. Wen e auocorrelaion a a imple form over a finie ime inerval, e ime omain can be eaier. Filer: u u anom Proce: (a) Fin e mean value of e oupu. (b) Fin e mean quare of e oupu. Fir: Coeren gain gain u u gain Oupu ignal erefore, gain
9 oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 9 of 6 C 8 o eliminae e abolue value, perform o inegral for eac par, n finally e auocorrelaion funcion (uing able) ep in j j ep in 4 4 in in in
10 oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 of 6 C 8 Poer pecral Deniy of a filere ie noie proce. Le aking e PD i ep i ep ep i ep i ep i
11 ime bae meo o collec yem ignal repone oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 of 6 C 8
12 ample: Wie oie Inpu Le For a ie noie proce, e mean quare (or n momen) i proporional o e filer poer. ignal-o-oie-aio (alay one for poer) P ignal i efine a Poie BQ i aume a e filer oe no cange e inpu ignal, bu ricly reuce e noie poer by e equivalen noie bani of e filer. e narroer e filer applie prior o ignal proceing, e greaer e of e ignal! erefore, alay apply an analog filer prior o proceing e ignal of inere! oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 of 6 C 8
13 oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 of 6 C 8 8- ample of Frequency-Domain nalyi oie in a linear feeback yem loop. Linear uperpoiion of o an o. ere are effecively o filer, one applie o an a econ apply o. an Generic efiniion of oupu Poer pecral Deniy:
14 Cange in e inpu o oupu ignal o noie raio. In Ou Ou B Q Were B Q If e noie i ae a e ignal inpu, e epece efiniion of noie equivalen bani reul. oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 4 of 6 C 8
15 eign noe: If i yem i in operaion, o mig you caracerize e ranfer funcion iou raically cange i normal operaion? Wa oul appen if you coul a a conrolle ie noie inpu? Given a you coul collec an compue e aiive inpu o oupu crocorrelaion, a mig you epec o fin? y a n a, for Perform e e i no noie an repea i noie an compare e reul. o oie, e epec for, Wi oie, e epec, for Can e fin e ifference an u e filer ep repone! ere are procee o caracerize running or operaing equipmen. ey valiae correc operaion! ey may provie an inicaion of impening problem or even failure! oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 5 of 6 C 8
16 8- umerical Compuaion of yem Oupu ee moifie CG for correlaion of earbea even an efining n even eecion reol. un e emonraion for M an FM. oie poer level an filering can grealy affec e reul of a yem. oe an figure are bae on or aken from maerial in e coure ebook: Probabiliic Meo of ignal an yem nalyi (r e.) by George. Cooper an Clare D. McGillem; Ofor Pre, 999. IB: B.J. Bazuin, pring 5 6 of 6 C 8
Design of Controller for Robot Position Control
eign of Conroller for Robo oiion Conrol Two imporan goal of conrol: 1. Reference inpu racking: The oupu mu follow he reference inpu rajecory a quickly a poible. Se-poin racking: Tracking when he reference
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,
u(t) Figure 1. Open loop control system
Open loop conrol v cloed loop feedbac conrol The nex wo figure preen he rucure of open loop and feedbac conrol yem Figure how an open loop conrol yem whoe funcion i o caue he oupu y o follow he reference
Let. x y. denote a bivariate time series with zero mean.
Linear Filer Le x y : T denoe a bivariae ime erie wih zero mean. Suppoe ha he ime erie {y : T} i conruced a follow: y a x The ime erie {y : T} i aid o be conruced from {x : T} by mean of a Linear Filer.
8.1. a) For step response, M input is u ( t) Taking inverse Laplace transform. as α 0. Ideal response, K c. = Kc Mτ D + For ramp response, 8-1
8. a For ep repone, inpu i u, U Y a U α α Y a α α Taking invere Laplae ranform a α e e / α / α A α 0 a δ 0 e / α a δ deal repone, α d Y i Gi U i δ Hene a α 0 a i For ramp repone, inpu i u, U Soluion anual
Single Phase Line Frequency Uncontrolled Rectifiers
Single Phae Line Frequency Unconrolle Recifier Kevin Gaughan 24-Nov-03 Single Phae Unconrolle Recifier 1 Topic Baic operaion an Waveform (nucive Loa) Power Facor Calculaion Supply curren Harmonic an Th
Chapter 9 - The Laplace Transform
Chaper 9 - The Laplace Tranform Selece Soluion. Skech he pole-zero plo an region of convergence (if i exi) for hee ignal. ω [] () 8 (a) x e u = 8 ROC σ ( ) 3 (b) x e co π u ω [] ( ) () (c) x e u e u ROC
Exponential Sawtooth
ECPE 36 HOMEWORK 3: PROPERTIES OF THE FOURIER TRANSFORM SOLUTION. Exponenial Sawooh: The eaie way o do hi problem i o look a he Fourier ranform of a ingle exponenial funcion, () = exp( )u(). From he able
EE Control Systems LECTURE 2
Copyrigh F.L. Lewi 999 All righ reerved EE 434 - Conrol Syem LECTURE REVIEW OF LAPLACE TRANSFORM LAPLACE TRANSFORM The Laplace ranform i very ueful in analyi and deign for yem ha are linear and ime-invarian
UT Austin, ECE Department VLSI Design 5. CMOS Gate Characteristics
La moule: CMOS Tranior heory Thi moule: DC epone Logic Level an Noie Margin Tranien epone Delay Eimaion Tranior ehavior 1) If he wih of a ranior increae, he curren will ) If he lengh of a ranior increae,
13.1 Circuit Elements in the s Domain Circuit Analysis in the s Domain The Transfer Function and Natural Response 13.
Chaper 3 The Laplace Tranform in Circui Analyi 3. Circui Elemen in he Domain 3.-3 Circui Analyi in he Domain 3.4-5 The Tranfer Funcion and Naural Repone 3.6 The Tranfer Funcion and he Convoluion Inegral
Chapter 6. Laplace Transforms
Chaper 6. Laplace Tranform Kreyzig by YHLee;45; 6- An ODE i reduced o an algebraic problem by operaional calculu. The equaion i olved by algebraic manipulaion. The reul i ranformed back for he oluion of
18.03SC Unit 3 Practice Exam and Solutions
Sudy Guide on Sep, Dela, Convoluion, Laplace You can hink of he ep funcion u() a any nice mooh funcion which i for < a and for > a, where a i a poiive number which i much maller han any ime cale we care
Chapter 6. Laplace Transforms
6- Chaper 6. Laplace Tranform 6.4 Shor Impule. Dirac Dela Funcion. Parial Fracion 6.5 Convoluion. Inegral Equaion 6.6 Differeniaion and Inegraion of Tranform 6.7 Syem of ODE 6.4 Shor Impule. Dirac Dela
(V 1. (T i. )- FrC p. ))= 0 = FrC p (T 1. (T 1s. )+ UA(T os. (T is
. Yu are repnible fr a reacr in which an exhermic liqui-phae reacin ccur. The fee mu be preheae he hrehl acivain emperaure f he caaly, bu he pruc ream mu be cle. T reuce uiliy c, yu are cniering inalling
, the. L and the L. x x. max. i n. It is easy to show that these two norms satisfy the following relation: x x n x = (17.3) max
ecure 8 7. Sabiliy Analyi For an n dimenional vecor R n, he and he vecor norm are defined a: = T = i n i (7.) I i eay o how ha hee wo norm aify he following relaion: n (7.) If a vecor i ime-dependen, hen
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
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signal & Syem Prof. Mark Fowler Noe Se #27 C-T Syem: Laplace Tranform Power Tool for yem analyi Reading Aignmen: Secion 6.1 6.3 of Kamen and Heck 1/18 Coure Flow Diagram The arrow here how concepual
Lecture 12. Aperture and Noise. Jaeha Kim Mixed-Signal IC and System Group (MICS) Seoul National University
Lecure. Aperure and Noie Analyi of locked omparaor Jaeha Kim Mixed-Signal I and Syem Group MIS Seoul Naional Univeriy jaeha@ieee.org locked omparaor a.k.a. regeneraive amplifier, ene-amplifier, flip-flop,
Sample Final Exam (finals03) Covering Chapters 1-9 of Fundamentals of Signals & Systems
Sample Final Exam Covering Chaper 9 (final04) Sample Final Exam (final03) Covering Chaper 9 of Fundamenal of Signal & Syem Problem (0 mar) Conider he caual opamp circui iniially a re depiced below. I LI
CHAPTER. Forced Equations and Systems { } ( ) ( ) 8.1 The Laplace Transform and Its Inverse. Transforms from the Definition.
CHAPTER 8 Forced Equaion and Syem 8 The aplace Tranform and I Invere Tranform from he Definiion 5 5 = b b {} 5 = 5e d = lim5 e = ( ) b {} = e d = lim e + e d b = (inegraion by par) = = = = b b ( ) ( )
Chapter Three Systems of Linear Differential Equations
Chaper Three Sysems of Linear Differenial Equaions In his chaper we are going o consier sysems of firs orer orinary ifferenial equaions. These are sysems of he form x a x a x a n x n x a x a x a n x n
6.302 Feedback Systems Recitation : Phase-locked Loops Prof. Joel L. Dawson
6.32 Feedback Syem Phae-locked loop are a foundaional building block for analog circui deign, paricularly for communicaion circui. They provide a good example yem for hi cla becaue hey are an excellen
CONTROL SYSTEMS. Chapter 10 : State Space Response
CONTROL SYSTEMS Chaper : Sae Space Repone GATE Objecive & Numerical Type Soluion Queion 5 [GATE EE 99 IIT-Bombay : Mark] Conider a econd order yem whoe ae pace repreenaion i of he form A Bu. If () (),
Instrumentation & Process Control
Chemical Engineering (GTE & PSU) Poal Correpondence GTE & Public Secor Inrumenaion & Proce Conrol To Buy Poal Correpondence Package call a -999657855 Poal Coure ( GTE & PSU) 5 ENGINEERS INSTITUTE OF INDI.
F (u) du. or f(t) = t
8.3 Topic 9: Impulses and dela funcions. Auor: Jeremy Orloff Reading: EP 4.6 SN CG.3-4 pp.2-5. Warmup discussion abou inpu Consider e rae equaion d + k = f(). To be specific, assume is in unis of d kilograms.
CHAPTER 3 SIGNALS & SYSTEMS. z -transform in the z -plane will be (A) 1 (B) 1 (D) (C) . The unilateral Laplace transform of tf() (A) s (B) + + (D) (C)
CHAPER SIGNALS & SYSEMS YEAR ONE MARK n n MCQ. If xn [ ] (/) (/) un [ ], hen he region of convergence (ROC) of i z ranform in he z plane will be (A) < z < (B) < z < (C) < z < (D) < z MCQ. he unilaeral
NODIA AND COMPANY. GATE SOLVED PAPER Electrical Engineering SIGNALS & SYSTEMS. Copyright By NODIA & COMPANY
No par of hi publicaion may be reproduced or diribued in any form or any mean, elecronic, mechanical, phoocopying, or oherie ihou he prior permiion of he auhor. GAE SOLVED PAPER Elecrical Engineering SIGNALS
Additional Exercises for Chapter What is the slope-intercept form of the equation of the line given by 3x + 5y + 2 = 0?
ddiional Eercises for Caper 5 bou Lines, Slopes, and Tangen Lines 39. Find an equaion for e line roug e wo poins (, 7) and (5, ). 4. Wa is e slope-inercep form of e equaion of e line given by 3 + 5y +
CONTROL SYSTEMS. Chapter 3 Mathematical Modelling of Physical Systems-Laplace Transforms. Prof.Dr. Fatih Mehmet Botsalı
CONTROL SYSTEMS Chaper Mahemaical Modelling of Phyical Syem-Laplace Tranform Prof.Dr. Faih Mehme Boalı Definiion Tranform -- a mahemaical converion from one way of hinking o anoher o make a problem eaier
Chapter 8 Objectives
haper 8 Engr8 ircui Analyi Dr uri Nelon haper 8 Objecive Be able o eermine he naural an he ep repone of parallel circui; Be able o eermine he naural an he ep repone of erie circui. Engr8 haper 8, Nilon
6.8 Laplace Transform: General Formulas
48 HAP. 6 Laplace Tranform 6.8 Laplace Tranform: General Formula Formula Name, ommen Sec. F() l{ f ()} e f () d f () l {F()} Definiion of Tranform Invere Tranform 6. l{af () bg()} al{f ()} bl{g()} Lineariy
Rough Paths and its Applications in Machine Learning
Pah ignaure Machine learning applicaion Rough Pah and i Applicaion in Machine Learning July 20, 2017 Rough Pah and i Applicaion in Machine Learning Pah ignaure Machine learning applicaion Hiory and moivaion
F This leads to an unstable mode which is not observable at the output thus cannot be controlled by feeding back.
Lecure 8 Las ime: Semi-free configuraion design This is equivalen o: Noe ns, ener he sysem a he same place. is fixed. We design C (and perhaps B. We mus sabilize if i is given as unsable. Cs ( H( s = +
PSAT/NMSQT PRACTICE ANSWER SHEET SECTION 3 EXAMPLES OF INCOMPLETE MARKS COMPLETE MARK B C D B C D B C D B C D B C D 13 A B C D B C D 11 A B C D B C D
PSTNMSQT PRCTICE NSWER SHEET COMPLETE MRK EXMPLES OF INCOMPLETE MRKS I i recommended a you ue a No pencil I i very imporan a you fill in e enire circle darkly and compleely If you cange your repone, erae
A Theoretical Model of a Voltage Controlled Oscillator
A Theoreical Model of a Volage Conrolled Ocillaor Yenming Chen Advior: Dr. Rober Scholz Communicaion Science Iniue Univeriy of Souhern California UWB Workhop, April 11-1, 6 Inroducion Moivaion The volage
The Quantum Theory of Atoms and Molecules: The Schrodinger equation. Hilary Term 2008 Dr Grant Ritchie
e Quanum eory of Aoms and Molecules: e Scrodinger equaion Hilary erm 008 Dr Gran Ricie An equaion for maer waves? De Broglie posulaed a every paricles as an associaed wave of waveleng: / p Wave naure of
Mon Apr 2: Laplace transform and initial value problems like we studied in Chapter 5
Mah 225-4 Week 2 April 2-6 coninue.-.3; alo cover par of.4-.5, EP 7.6 Mon Apr 2:.-.3 Laplace ranform and iniial value problem like we udied in Chaper 5 Announcemen: Warm-up Exercie: Recall, The Laplace
EE 301 Lab 2 Convolution
EE 301 Lab 2 Convoluion 1 Inroducion In his lab we will gain some more experience wih he convoluion inegral and creae a scrip ha shows he graphical mehod of convoluion. 2 Wha you will learn This lab will
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,
s-domain Circuit Analysis
Domain ircui Analyi Operae direcly in he domain wih capacior, inducor and reior Key feaure lineariy i preerved c decribed by ODE and heir I Order equal number of plu number of Elemenbyelemen and ource
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signals & Sysems Prof. Mar Fowler Noe Se #1 C-T Signals: Circuis wih Periodic Sources 1/1 Solving Circuis wih Periodic Sources FS maes i easy o find he response of an RLC circui o a periodic source!
Interpolation and Pulse Shaping
EE345S Real-Time Digial Signal Proceing Lab Spring 2006 Inerpolaion and Pule Shaping Prof. Brian L. Evan Dep. of Elecrical and Compuer Engineering The Univeriy of Texa a Auin Lecure 7 Dicree-o-Coninuou
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
6 December 2013 H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 1
Lecure Noe Fundamenal of Conrol Syem Inrucor: Aoc. Prof. Dr. Huynh Thai Hoang Deparmen of Auomaic Conrol Faculy of Elecrical & Elecronic Engineering Ho Chi Minh Ciy Univeriy of Technology Email: hhoang@hcmu.edu.vn
Serial : 4LS1_A_EC_Signal & Systems_230918
Serial : LS_A_EC_Signal & Syem_8 CLASS TEST (GATE) Delhi oida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubanewar Kolkaa Pana Web: E-mail: info@madeeay.in Ph: -56 CLASS TEST 8- ELECTROICS EGIEERIG Subjec
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
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
Data Fusion using Kalman Filter. Ioannis Rekleitis
Daa Fusion using Kalman Filer Ioannis Rekleiis Eample of a arameerized Baesian Filer: Kalman Filer Kalman filers (KF represen poserior belief b a Gaussian (normal disribuion A -d Gaussian disribuion is
Module II, Part C. More Insight into Fiber Dispersion
Moule II Par C More Insigh ino Fiber Dispersion . Polariaion Moe Dispersion Fiber Birefringence: Imperfec cylinrical symmery leas o wha is known as birefringence. Recall he HE moe an is E x componen which
Chapter 2: Principles of steady-state converter analysis
Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
Demodulation of Digitally Modulated Signals
Addiional maerial for TSKS1 Digial Communicaion and TSKS2 Telecommunicaion Demodulaion of Digially Modulaed Signals Mikael Olofsson Insiuionen för sysemeknik Linköpings universie, 581 83 Linköping November
ECE Spring Prof. David R. Jackson ECE Dept. Notes 39
ECE 6341 Spring 2016 Prof. David R. Jackon ECE Dep. Noe 39 1 Finie Source J ( y, ) For a phaed curren hee: p p j( k kyy) J y = J e + (, ) 0 The angenial elecric field ha i produced i: ( p ˆ ˆ) j( k + k
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 30 Signal & Syem Prof. ark Fowler oe Se #34 C-T Tranfer Funcion and Frequency Repone /4 Finding he Tranfer Funcion from Differenial Eq. Recall: we found a DT yem Tranfer Funcion Hz y aking he ZT of
More on ODEs by Laplace Transforms October 30, 2017
More on OE b Laplace Tranfor Ocober, 7 More on Ordinar ifferenial Equaion wih Laplace Tranfor Larr areo Mechanical Engineering 5 Seinar in Engineering nali Ocober, 7 Ouline Review la cla efiniion of Laplace
Laplace Transform. Inverse Laplace Transform. e st f(t)dt. (2)
Laplace Tranform Maoud Malek The Laplace ranform i an inegral ranform named in honor of mahemaician and aronomer Pierre-Simon Laplace, who ued he ranform in hi work on probabiliy heory. I i a powerful
EE202 Circuit Theory II
EE202 Circui Theory II 2017-2018, Spring Dr. Yılmaz KALKAN I. Inroducion & eview of Fir Order Circui (Chaper 7 of Nilon - 3 Hr. Inroducion, C and L Circui, Naural and Sep epone of Serie and Parallel L/C
Switching Characteristics of Power Devices
Swiching Characeriic of Power Device Device uilizaion can be grealy improved by underanding he device wiching charcaeriic. he main performance wiching characeriic of power device: he ave operaing area
Additional Methods for Solving DSGE Models
Addiional Mehod for Solving DSGE Model Karel Meren, Cornell Univeriy Reference King, R. G., Ploer, C. I. & Rebelo, S. T. (1988), Producion, growh and buine cycle: I. he baic neoclaical model, Journal of
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
Sensors, Signals and Noise
Sensors, Signals and Noise COURSE OUTLINE Inroducion Signals and Noise: 1) Descripion Filering Sensors and associaed elecronics rv 2017/02/08 1 Noise Descripion Noise Waveforms and Samples Saisics of Noise
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
Characteristics of Linear System
Characerisics o Linear Sysem h g h : Impulse response F G : Frequency ranser uncion Represenaion o Sysem in ime an requency. Low-pass iler g h G F he requency ranser uncion is he Fourier ransorm o he impulse
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
D.I. Survival models and copulas
D- D. SURVIVAL COPULA D.I. Survival moels an copulas Definiions, relaionships wih mulivariae survival isribuion funcions an relaionships beween copulas an survival copulas. D.II. Fraily moels Use of a
Comparison between the Discrete and Continuous Time Models
Comparison beween e Discree and Coninuous Time Models D. Sulsky June 21, 2012 1 Discree o Coninuous Recall e discree ime model Î = AIS Ŝ = S Î. Tese equaions ell us ow e populaion canges from one day o
Problem Set If all directed edges in a network have distinct capacities, then there is a unique maximum flow.
CSE 202: Deign and Analyi of Algorihm Winer 2013 Problem Se 3 Inrucor: Kamalika Chaudhuri Due on: Tue. Feb 26, 2013 Inrucion For your proof, you may ue any lower bound, algorihm or daa rucure from he ex
Lecture 6 - Testing Restrictions on the Disturbance Process (References Sections 2.7 and 2.10, Hayashi)
Lecure 6 - esing Resricions on he Disurbance Process (References Secions 2.7 an 2.0, Hayashi) We have eveloe sufficien coniions for he consisency an asymoic normaliy of he OLS esimaor ha allow for coniionally
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
Web Appendix N - Derivations of the Properties of the LaplaceTransform
M. J. Robers - 2/18/07 Web Appenix N - Derivaions of he Properies of he aplacetransform N.1 ineariy e z= x+ y where an are consans. Then = x+ y Zs an he lineariy propery is N.2 Time Shifing es = xe s +
Chapter 2 The Derivative Applied Calculus 97
Caper Te Derivaive Applie Calculus 97 Secion 3: Power an Sum Rules for Derivaives In e ne few secions, we ll ge e erivaive rules a will le us fin formulas for erivaives wen our funcion comes o us as a
L1, L2, N1 N2. + Vout. C out. Figure 2.1.1: Flyback converter
page 11 Flyback converer The Flyback converer belongs o he primary swiched converer family, which means here is isolaion beween in and oupu. Flyback converers are used in nearly all mains supplied elecronic
ADDITIONAL PROBLEMS (a) Find the Fourier transform of the half-cosine pulse shown in Fig. 2.40(a). Additional Problems 91
ddiional Problems 9 n inverse relaionship exiss beween he ime-domain and freuency-domain descripions of a signal. Whenever an operaion is performed on he waveform of a signal in he ime domain, a corresponding
( ) ( ) 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
3. Several Random Variables
. Several Random Variables. Two Random Variables. Conditional Probabilit--Revisited. Statistical Independence.4 Correlation between Random Variables. Densit unction o the Sum o Two Random Variables. Probabilit
Embedded Systems and Software. A Simple Introduction to Embedded Control Systems (PID Control)
Embedded Sysems and Sofware A Simple Inroducion o Embedded Conrol Sysems (PID Conrol) Embedded Sysems and Sofware, ECE:3360. The Universiy of Iowa, 2016 Slide 1 Acknowledgemens The maerial in his lecure
The complex Fourier series has an important limiting form when the period approaches infinity, i.e., T 0. 0 since it is proportional to 1/L, but
Fourier Transforms The complex Fourier series has an imporan limiing form when he period approaches infiniy, i.e., T or L. Suppose ha in his limi () k = nπ L remains large (ranging from o ) and (2) c n
CHEMISTRY 047 STUDY PACKAGE
CHEMISTRY 047 STUDY PACKAGE Tis maerial is inended as a review of skills you once learned. PREPARING TO WRITE THE ASSESSMENT VIU/CAP/D:\Users\carpenem\AppDaa\Local\Microsof\Windows\Temporary Inerne Files\Conen.Oulook\JTXREBLD\Cemisry
Advanced Integration Techniques: Integration by Parts We may differentiate the product of two functions by using the product rule:
Avance Inegraion Techniques: Inegraion by Pars We may iffereniae he prouc of wo funcions by using he prouc rule: x f(x)g(x) = f (x)g(x) + f(x)g (x). Unforunaely, fining an anierivaive of a prouc is no
The Rosenblatt s LMS algorithm for Perceptron (1958) is built around a linear neuron (a neuron with a linear
In The name of God Lecure4: Percepron and AALIE r. Majid MjidGhoshunih Inroducion The Rosenbla s LMS algorihm for Percepron 958 is buil around a linear neuron a neuron ih a linear acivaion funcion. Hoever,
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
d 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3
and d = c b - b c c d = c b - b c c This process is coninued unil he nh row has been compleed. The complee array of coefficiens is riangular. Noe ha in developing he array an enire row may be divided or
THE CATCH PROCESS (continued)
THE CATCH PROCESS (coninued) In our previous derivaion of e relaionsip beween CPUE and fis abundance we assumed a all e fising unis and all e fis were spaially omogeneous. Now we explore wa appens wen
6.003 Homework #9 Solutions
6.00 Homework #9 Soluions Problems. Fourier varieies a. Deermine he Fourier series coefficiens of he following signal, which is periodic in 0. x () 0 0 a 0 5 a k sin πk 5 sin πk 5 πk for k 0 a k 0 πk j
Linear Circuit Elements
1/25/2011 inear ircui Elemens.doc 1/6 inear ircui Elemens Mos microwave devices can be described or modeled in erms of he hree sandard circui elemens: 1. ESISTANE () 2. INDUTANE () 3. APAITANE () For he
ANSWERS TO SELECTED EXCERCISES, CH 18-27
Eercise 8. The moifie version of pr7_.m for he 5-55 banpass filer using a n orer Buerworh an is oupu graph. To moify he scrip for he 5-5 ban change he values in he buer comman below i.e.: [b a]=buer[5/500
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
This document was generated at 1:04 PM, 09/10/13 Copyright 2013 Richard T. Woodward. 4. End points and transversality conditions AGEC
his documen was generaed a 1:4 PM, 9/1/13 Copyrigh 213 Richard. Woodward 4. End poins and ransversaliy condiions AGEC 637-213 F z d Recall from Lecure 3 ha a ypical opimal conrol problem is o maimize (,,
EEC 118 Lecture #15: Interconnect. Rajeevan Amirtharajah University of California, Davis
EEC 118 Lecure #15: Inerconnec Rajeevan Amiraraja Universiy of California, Davis Ouline Review and Finis: Low Power Design Inerconnec Effecs: Rabaey C. 4 and C. 9 (Kang & Leblebici, 6.5-6.6) Amiraraja,
Algorithms and Data Structures 2011/12 Week 9 Solutions (Tues 15th - Fri 18th Nov)
Algorihm and Daa Srucure 2011/ Week Soluion (Tue 15h - Fri 18h No) 1. Queion: e are gien 11/16 / 15/20 8/13 0/ 1/ / 11/1 / / To queion: (a) Find a pair of ube X, Y V uch ha f(x, Y) = f(v X, Y). (b) Find
Macroeconomics 1. Ali Shourideh. Final Exam
4780 - Macroeconomic 1 Ali Shourideh Final Exam Problem 1. A Model of On-he-Job Search Conider he following verion of he McCall earch model ha allow for on-he-job-earch. In paricular, uppoe ha ime i coninuou
Chapter 3 : Transfer Functions Block Diagrams Signal Flow Graphs
Chapter 3 : Tranfer Function Block Diagram Signal Flow Graph 3.. Tranfer Function 3.. Block Diagram of Control Sytem 3.3. Signal Flow Graph 3.4. Maon Gain Formula 3.5. Example 3.6. Block Diagram to Signal
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)
Diebold, Chapter 7. Francis X. Diebold, Elements of Forecasting, 4th Edition (Mason, Ohio: Cengage Learning, 2006). Chapter 7. Characterizing Cycles
Diebold, Chaper 7 Francis X. Diebold, Elemens of Forecasing, 4h Ediion (Mason, Ohio: Cengage Learning, 006). Chaper 7. Characerizing Cycles Afer compleing his reading you should be able o: Define covariance
Chapter 4. Truncation Errors
Chaper 4. Truncaion Errors and he Taylor Series Truncaion Errors and he Taylor Series Non-elemenary funcions such as rigonomeric, eponenial, and ohers are epressed in an approimae fashion using Taylor
Stable block Toeplitz matrix for the processing of multichannel seismic data
Indian Journal of Marine Sciences Vol. 33(3), Sepember 2004, pp. 215-219 Sable block Toepliz marix for he processing of mulichannel seismic daa Kiri Srivasava* & V P Dimri Naional Geophysical Research
Application of Simultaneous Equation in Finance Research
Applicaion of Simulaneou Equaion in Finance Reearch By Carl R. Chen an Cheng Few Lee A. Inroucion Empirical finance reearch ofen employ a ingle equaion for eimaion an eing. However, ingle equaion rarely
V L. DT s D T s t. Figure 1: Buck-boost converter: inductor current i(t) in the continuous conduction mode.
ECE 445 Analysis and Design of Power Elecronic Circuis Problem Se 7 Soluions Problem PS7.1 Erickson, Problem 5.1 Soluion (a) Firs, recall he operaion of he buck-boos converer in he coninuous conducion
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
Piecewise-Defined Functions and Periodic Functions
28 Piecewie-Defined Funcion and Periodic Funcion A he ar of our udy of he Laplace ranform, i wa claimed ha he Laplace ranform i paricularly ueful when dealing wih nonhomogeneou equaion in which he forcing