Current Mode Winner-Take-All Circuits Shih-Chii Liu. Translinear Principle. Current-Mode Low-Pass Filter. Translinear Principle
|
|
- Matthew Harrison
- 6 years ago
- Views:
Transcription
1 NE Lecture 6 Wier-Take-All 0/9/03 Curret Mode Wier-Take-All Circuits Shih-Chii Liu Outlie: Trasliear Priciple Curret-Mode Circuit Fuctios: Low-Pass Temporal Filter PseudoCoductaces Spatial Filteri Resistive Networks Curret Coveyor as Curret Mirror Normalizer Circuit 0/9/03 Wier-Take-All Circuits Trasliear Priciple Coied by Barrie Gilbert i 975, trasliear meas that the bipolar juctio trasistor s trascoductace is liear i its collector curret. a bipolar trasistor, the collector curret is expoetial i the baseemitter voltae. This expoetial depedece is also captured i the subthreshold domai of a MOSFET. Trasliear Priciple Curret-Mode Low-Pass Filter Kirchhoff's oltae Law aroud loop: CCW CW ( Substituti for i ( : UT lo UT lo CCW 0 CW 0 CCW CW (Frey, 98 Curret-Mode Low-Pass Filter PseudoCoductace Pseudo: bei apparetly rather tha actually as stated ( ( * * * s d * f s f d ( ( ( / UT s / UT d / UT 0 e ( e e s d (Frey, 98 PseudoCoductace 0/9/03 6 Neuromorphic Eieeri 03
2 NE Lecture 6 Wier-Take-All 0/9/03 Curret Divider i Basic Elemet of Pseudo-Resistive (Diffusor Network w e w ( / U T w ( e / UT c / UT 0 w e ( e / UT c / UT 0 Ratios of currets: 0/9/03 8 e R R =( - =(R -R =R( - i s T d i / UT s / UT d / UT 0 ( ( s/ UT ( d / UT 0 T e e e ( e e 0/9/03 9 Diffusor What if ates are at differet potetials? t l t t trasverse l lateral l l l e l l ( t l e t t e e l l ( t l Pseudocoductace! ( 0/9/03 t t j- R Diffusor Network j- outj- R outj j+ outj+ 0/9/03 j ij j j+ R Diffusor Network Curret Coveyor G j- G j- ij G j j j+ G y y z z z x x l y outj- outj outj+ R R R ( GR/ UT e ( out j out j out j out j i j d out x out x i x e ( /U G R T ( ( ( ; dx x x Used i Low-pass filters Multiplier circuits Wier-take-all circuits 0/9/03 3 0/9/03 4 Neuromorphic Eieeri 03
3 NE Lecture 6 Wier-Take-All 0/9/03 Curret Coveyor as a Multiplier y y z w x Usi trasliear priciple: z x y xw y 0 0 w x y w z z x y w Curret Coveyor as a Curret Mirror y Z Y X y y x y y y x w 0/9/03 5 0/9/03 6 Gilbert Normalizer WTA Networks d i out i d out di / UT ii 0e dic/ UT c/ U outi 0e iie T b outi i outi b ii i ii A WTA mechaism is a device that determies the idetity ad sometimes the amplitude, of its larest iput. This mechaism is ecessary to eforce competitio betwee differet possible outputs of a etwork. A variat, called softmax, assis each iput a weiht so that all weihts sum to ad the larest iput has the larest weiht. The WTA is the limiti case of the softmax. b b 0/9/03 7 0/9/03 9 Software Simulatios put Output 0/9/03 0 0/9/03 Neuromorphic Eieeri 03 3
4 NE Lecture 6 Wier-Take-All 0/9/03 Curret-Mode WTA Circuit A Buffered Curret Mirror A cotiuous-time aalo circuit that receives aalo iputs ad implemets the WTA fuctio. t was oriially desied by Lazzaro et al. i 989. out? Acts like curret sik M i? Source follower follows out 0/9/03 b out oes to where it eeds to be to make o to where it eeds to be to make M i sik 0/9/03 3 A Buffered Curret Mirror Acts like curret sik out? d M i? d b out out 0/9/03 4 0/9/03 5 out out ecodes max(, What happes whe <? b << follows the hiher of ad 0/9/03 6 ecodes max(, out =0, out = b 0/9/03 7 Neuromorphic Eieeri 03 4
5 NE Lecture 6 Wier-Take-All 0/9/03 f >, ecodes i d i i out out i d b b out out out 0/9/03 8 0/9/03 9 WTA Circuit A N-Cell WTA Assume iputs are iitially equal, that is,. i i i out out i Now let, i positive chae i voltae at ode (also eative chae i voltae at ode E d out 0 i e U / T d d d M 3 M 4 M M b d i out i out i3 out3 i4 out4 0/9/ /9/03 3 Hysteretic WTA WTA Circuits i Lab i out out i b b b diveri (997 0/9/03 3 Morris, Horiuchi, DeWeerth (998 WTA HWTA 0/9/03 33 Neuromorphic Eieeri 03 5
6 NE Lecture 6 Wier-Take-All 0/9/03 The Ed 0/9/03 34 Neuromorphic Eieeri 03 6
Bipolar Junction Transistors
ipolar Juctio Trasistors ipolar juctio trasistor (JT) was iveted i 948 at ell Telephoe Laboratories Sice 97, the high desity ad low power advatage of the MOS techology steadily eroded the JT s early domiace.
More informationLecture 8. Nonlinear Device Stamping
PRINCIPLES OF CIRCUIT SIMULATION Lecture 8. Noliear Device Stampig Guoyog Shi, PhD shiguoyog@ic.sjtu.edu.c School of Microelectroics Shaghai Jiao Tog Uiversity Fall -- Slide Outlie Solvig a oliear circuit
More informationResponse Analysis on Nonuniform Transmission Line
SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. No. November 5 173-18 Respose Aalysis o Nouiform Trasmissio Lie Zlata Cvetković 1 Slavoljub Aleksić Bojaa Nikolić 3 Abstract: Trasiets o a lossless epoetial
More informationVoltage controlled oscillator (VCO)
Voltage cotrolled oscillator (VO) Oscillatio frequecy jl Z L(V) jl[ L(V)] [L L (V)] L L (V) T VO gai / Logf Log 4 L (V) f f 4 L(V) Logf / L(V) f 4 L (V) f (V) 3 Lf 3 VO gai / (V) j V / V Bi (V) / V Bi
More information1. Linearization of a nonlinear system given in the form of a system of ordinary differential equations
. Liearizatio of a oliear system give i the form of a system of ordiary differetial equatios We ow show how to determie a liear model which approximates the behavior of a time-ivariat oliear system i a
More informationSignal Processing. Lecture 02: Discrete Time Signals and Systems. Ahmet Taha Koru, Ph. D. Yildiz Technical University.
Sigal Processig Lecture 02: Discrete Time Sigals ad Systems Ahmet Taha Koru, Ph. D. Yildiz Techical Uiversity 2017-2018 Fall ATK (YTU) Sigal Processig 2017-2018 Fall 1 / 51 Discrete Time Sigals Discrete
More informationFrequency Domain Filtering
Frequecy Domai Filterig Raga Rodrigo October 19, 2010 Outlie Cotets 1 Itroductio 1 2 Fourier Represetatio of Fiite-Duratio Sequeces: The Discrete Fourier Trasform 1 3 The 2-D Discrete Fourier Trasform
More information, then cv V. Differential Equations Elements of Lineaer Algebra Name: Consider the differential equation. and y2 cos( kx)
Cosider the differetial equatio y '' k y 0 has particular solutios y1 si( kx) ad y cos( kx) I geeral, ay liear combiatio of y1 ad y, cy 1 1 cy where c1, c is also a solutio to the equatio above The reaso
More informationContinuous Functions
Cotiuous Fuctios Q What does it mea for a fuctio to be cotiuous at a poit? Aswer- I mathematics, we have a defiitio that cosists of three cocepts that are liked i a special way Cosider the followig defiitio
More informationWhy analog microelectronics?
hy aalo microelectroics? iital is taki over? Yes, but electrical sials are fudametally aalo! Aalo desi has prove fudametal for hihquality desi of complex systems Mixed-mode systems Natural sials are aalo
More informationBasic Physics of Semiconductors
Chater 2 Basic Physics of Semicoductors 2.1 Semicoductor materials ad their roerties 2.2 PN-juctio diodes 2.3 Reverse Breakdow 1 Semicoductor Physics Semicoductor devices serve as heart of microelectroics.
More informationELEC1200: A System View of Communications: from Signals to Packets Lecture 3
ELEC2: A System View of Commuicatios: from Sigals to Packets Lecture 3 Commuicatio chaels Discrete time Chael Modelig the chael Liear Time Ivariat Systems Step Respose Respose to sigle bit Respose to geeral
More informationBasic Physics of Semiconductors
Chater 2 Basic Physics of Semicoductors 2.1 Semicoductor materials ad their roerties 2.2 PN-juctio diodes 2.3 Reverse Breakdow 1 Semicoductor Physics Semicoductor devices serve as heart of microelectroics.
More informationCS151 Complexity Theory
Time ad Space CS151 Complexity Theory Lecture 2 April 1, 2004 A motivatig questio: Boolea formula with odes evaluate usig O(log ) space? depth-first traversal requires storig itermediate values idea: short-circuit
More informationTracking Performance of the MMax Conjugate Gradient Algorithm Bei Xie and Tamal Bose
racki Performace of the MMa Cojuate Gradiet Alorithm Bei Xie ad amal Bose Wireless@V Bradley Det. of Electrical ad Comuter Eieeri Viriia ech Outlie Motivatio Backroud Cojuate Gradiet CG Alorithm Partial
More informationWeek 1, Lecture 2. Neural Network Basics. Announcements: HW 1 Due on 10/8 Data sets for HW 1 are online Project selection 10/11. Suggested reading :
ME 537: Learig-Based Cotrol Week 1, Lecture 2 Neural Network Basics Aoucemets: HW 1 Due o 10/8 Data sets for HW 1 are olie Proect selectio 10/11 Suggested readig : NN survey paper (Zhag Chap 1, 2 ad Sectios
More informationFast Power Flow Methods 1.0 Introduction
Fast ower Flow Methods. Itroductio What we have leared so far is the so-called full- ewto-raphso R power flow alorithm. The R alorithm is perhaps the most robust alorithm i the sese that it is most liely
More information2D DSP Basics: 2D Systems
- Digital Image Processig ad Compressio D DSP Basics: D Systems D Systems T[ ] y = T [ ] Liearity Additivity: If T y = T [ ] The + T y = y + y Homogeeity: If The T y = T [ ] a T y = ay = at [ ] Liearity
More informationPhysics 310 Lecture 9a DAC and ADC
Lecture 9a ad Mo. 3/19 Wed. 3/1 Thurs. 3/ Fri. 3/3 Mo. 3/6 Wed. 3/8 Thurs. 3/9 h 14.1,.6-.10; pp 373-374 (Samplig Frequecy); 1.6: & More of the same Lab 9: & More of the same; Quiz h 14 Project: ompoet
More informationLinear time invariant systems
Liear time ivariat systems Alejadro Ribeiro Dept. of Electrical ad Systems Egieerig Uiversity of Pesylvaia aribeiro@seas.upe.edu http://www.seas.upe.edu/users/~aribeiro/ February 25, 2016 Sigal ad Iformatio
More informationADVANCED DIGITAL SIGNAL PROCESSING
ADVANCED DIGITAL SIGNAL PROCESSING PROF. S. C. CHAN (email : sccha@eee.hku.hk, Rm. CYC-702) DISCRETE-TIME SIGNALS AND SYSTEMS MULTI-DIMENSIONAL SIGNALS AND SYSTEMS RANDOM PROCESSES AND APPLICATIONS ADAPTIVE
More informationSOME ASPECTS OF MEASUREMENT ERRORS ANALYSIS IN ELECTROMAGNETIC FLOW METERS FOR OPEN CHANNELS
OME APECT OF MEAUREMENT ERROR ANALYI IN ELECTROMAGNETIC FLOW METER FOR OPEN CHANNEL Adrzej Michalski () Wiesław Piotrowski () () Warsaw Uiversity of Techoloy, Istitute of the Theory of Electrical Eieeri
More informationln(i G ) 26.1 Review 26.2 Statistics of multiple breakdowns M Rows HBD SBD N Atoms Time
EE650R: Reliability Physics of Naoelectroic Devices Lecture 26: TDDB: Statistics of Multiple Breadows Date: Nov 17, 2006 ClassNotes: Jaydeep P. Kulari Review: Pradeep R. Nair 26.1 Review I the last class
More informationPRELIM PROBLEM SOLUTIONS
PRELIM PROBLEM SOLUTIONS THE GRAD STUDENTS + KEN Cotets. Complex Aalysis Practice Problems 2. 2. Real Aalysis Practice Problems 2. 4 3. Algebra Practice Problems 2. 8. Complex Aalysis Practice Problems
More informationLECTURE 17: Linear Discriminant Functions
LECURE 7: Liear Discrimiat Fuctios Perceptro leari Miimum squared error (MSE) solutio Least-mea squares (LMS) rule Ho-Kashyap procedure Itroductio to Patter Aalysis Ricardo Gutierrez-Osua exas A&M Uiversity
More information5.61 Fall 2013 Problem Set #3
5.61 Fall 013 Problem Set #3 1. A. McQuarrie, page 10, #3-3. B. McQuarrie, page 10, #3-4. C. McQuarrie, page 18, #4-11.. McQuarrie, pages 11-1, #3-11. 3. A. McQuarrie, page 13, #3-17. B. McQuarrie, page
More informationAntenna Engineering Lecture 8: Antenna Arrays
Atea Egieerig Lecture 8: Atea Arrays ELCN45 Sprig 211 Commuicatios ad Computer Egieerig Program Faculty of Egieerig Cairo Uiversity 2 Outlie 1 Array of Isotropic Radiators Array Cofiguratios The Space
More informationPH 411/511 ECE B(k) Sin k (x) dk (1)
Fall-26 PH 4/5 ECE 598 A. La Rosa Homework-2 Due -3-26 The Homework is iteded to gai a uderstadig o the Heiseberg priciple, based o a compariso betwee the width of a pulse ad the width of its spectral
More informationECEN474: (Analog) VLSI Circuit Design Fall 2012
EEN474: (Aalo) VS ircuit Desi Fall 0 ecture 3: Three urret Mirror OTA Sa Palero Aalo & Mixed-Sial eter Texas A&M Uiersity Aouceets & Aeda H4 due edesday 0/3 Exa Friday / Siple OTA Reiew Three urret Mirror
More informationMath 312 Lecture Notes One Dimensional Maps
Math 312 Lecture Notes Oe Dimesioal Maps Warre Weckesser Departmet of Mathematics Colgate Uiversity 21-23 February 25 A Example We begi with the simplest model of populatio growth. Suppose, for example,
More informationCrash course part 2. Frequency compensation
Crash course part Frequecy compesatio Ageda Frequecy depedace Feedback amplifiers Frequecy depedace of the Trasistor Frequecy Compesatio Phatom Zero Examples Crash course part poles ad zeros I geeral a
More information15-780: Graduate Artificial Intelligence. Density estimation
5-780: Graduate Artificial Itelligece Desity estimatio Coditioal Probability Tables (CPT) But where do we get them? P(B)=.05 B P(E)=. E P(A B,E) )=.95 P(A B, E) =.85 P(A B,E) )=.5 P(A B, E) =.05 A P(J
More informationSHANGHAI JIAO TONG UNIVERSITY LECTURE
SHANGHAI JIAO TONG UNIVERSITY LECTURE 9 2017 Athoy J. Leggett Departmet of Physics Uiversity of Illiois at Urbaa-Champaig, USA ad Director, Ceter for Complex Physics Shaghai Jiao Tog Uiversity SJTU 9.1
More informationME 539, Fall 2008: Learning-Based Control
ME 539, Fall 2008: Learig-Based Cotrol Neural Network Basics 10/1/2008 & 10/6/2008 Uiversity Orego State Neural Network Basics Questios??? Aoucemet: Homework 1 has bee posted Due Friday 10/10/08 at oo
More informationParasitic Resistance L R W. Polysilicon gate. Drain. contact L D. V GS,eff R S R D. Drain
Parasitic Resistace G Polysilico gate rai cotact V GS,eff S R S R S, R S, R + R C rai Short Chael Effects Chael-egth Modulatio Equatio k ( V V ) GS T suggests that the trasistor i the saturatio mode acts
More informationELEG 4603/5173L Digital Signal Processing Ch. 1 Discrete-Time Signals and Systems
Departmet of Electrical Egieerig Uiversity of Arasas ELEG 4603/5173L Digital Sigal Processig Ch. 1 Discrete-Time Sigals ad Systems Dr. Jigxia Wu wuj@uar.edu OUTLINE 2 Classificatios of discrete-time sigals
More informationEE415/515 Fundamentals of Semiconductor Devices Fall 2012
090 EE4555 Fudaetals of Seicoductor evices Fall 0 ecture : MOSFE hapter 0.3, 0.4 090 J. E. Morris Reider: Here is what the MOSFE looks like 090 N-chael MOSFEs: Ehaceet & epletio odes 090 J. E. Morris 3
More informationSequences A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence
Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece 1, 1, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet
More informationReview Questions, Chapters 8, 9. f(y) = 0, elsewhere. F (y) = f Y(1) = n ( e y/θ) n 1 1 θ e y/θ = n θ e yn
Stat 366 Lab 2 Solutios (September 2, 2006) page TA: Yury Petracheko, CAB 484, yuryp@ualberta.ca, http://www.ualberta.ca/ yuryp/ Review Questios, Chapters 8, 9 8.5 Suppose that Y, Y 2,..., Y deote a radom
More informationFREE VIBRATION RESPONSE OF A SYSTEM WITH COULOMB DAMPING
Mechaical Vibratios FREE VIBRATION RESPONSE OF A SYSTEM WITH COULOMB DAMPING A commo dampig mechaism occurrig i machies is caused by slidig frictio or dry frictio ad is called Coulomb dampig. Coulomb dampig
More informationPosted-Price, Sealed-Bid Auctions
Posted-Price, Sealed-Bid Auctios Professors Greewald ad Oyakawa 207-02-08 We itroduce the posted-price, sealed-bid auctio. This auctio format itroduces the idea of approximatios. We describe how well this
More informationPH 411/511 ECE B(k) Sin k (x) dk (1)
Fall-27 PH 4/5 ECE 598 A. La Rosa Homework-3 Due -7-27 The Homework is iteded to gai a uderstadig o the Heiseberg priciple, based o a compariso betwee the width of a pulse ad the width of its spectral
More informationIntroduction to Signals and Systems, Part V: Lecture Summary
EEL33: Discrete-Time Sigals ad Systems Itroductio to Sigals ad Systems, Part V: Lecture Summary Itroductio to Sigals ad Systems, Part V: Lecture Summary So far we have oly looked at examples of o-recursive
More informationLecture #5: Begin Quantum Mechanics: Free Particle and Particle in a 1D Box
561 Fall 013 Lecture #5 page 1 Last time: Lecture #5: Begi Quatum Mechaics: Free Particle ad Particle i a 1D Box u 1 u 1-D Wave equatio = x v t * u(x,t): displacemets as fuctio of x,t * d -order: solutio
More informationMinimum Source/Drain Area AS,AD = (0.48µm)(0.60µm) - (0.12µm)(0.12µm) = µm 2
UNIERSITY OF CALIFORNIA College of Egieerig Departmet of Electrical Egieerig ad Computer Scieces Last modified o February 1 st, 005 by Chris Baer (crbaer@eecs Adrei ladimirescu Homewor #3 EECS141 Due Friday,
More informationSTAT Homework 1 - Solutions
STAT-36700 Homework 1 - Solutios Fall 018 September 11, 018 This cotais solutios for Homework 1. Please ote that we have icluded several additioal commets ad approaches to the problems to give you better
More informationWavelets and filterbanks. Mallat 2009, Chapter 7
Wavelets ad filterbaks Mallat 2009, Capter 7 Outlie Wavelets ad Filterbaks Biortooal bases Te dual perspective: from FB to wavelet bases Biortooal FB Perfect recostructio coditios Separable bases 2D Overcomplete
More informationCMOS. Dynamic Logic Circuits. Chapter 9. Digital Integrated Circuits Analysis and Design
MOS Digital Itegrated ircuits Aalysis ad Desig hapter 9 Dyamic Logic ircuits 1 Itroductio Static logic circuit Output correspodig to the iput voltage after a certai time delay Preservig its output level
More informationf(x)g(x) dx is an inner product on D.
Ark9: Exercises for MAT2400 Fourier series The exercises o this sheet cover the sectios 4.9 to 4.13. They are iteded for the groups o Thursday, April 12 ad Friday, March 30 ad April 13. NB: No group o
More informationThe aim of the course is to give an introduction to semiconductor device physics. The syllabus for the course is:
Semicoductor evices Prof. Rb Robert tat A. Taylor The aim of the course is to give a itroductio to semicoductor device physics. The syllabus for the course is: Simple treatmet of p- juctio, p- ad p-i-
More informationMTH 122 Calculus II Essex County College Division of Mathematics and Physics 1 Lecture Notes #20 Sakai Web Project Material
MTH 1 Calculus II Essex Couty College Divisio of Mathematics ad Physics 1 Lecture Notes #0 Sakai Web Project Material 1 Power Series 1 A power series is a series of the form a x = a 0 + a 1 x + a x + a
More informationCHAPTER 1 SEQUENCES AND INFINITE SERIES
CHAPTER SEQUENCES AND INFINITE SERIES SEQUENCES AND INFINITE SERIES (0 meetigs) Sequeces ad limit of a sequece Mootoic ad bouded sequece Ifiite series of costat terms Ifiite series of positive terms Alteratig
More informationhttp://www.xelca.l/articles/ufo_ladigsbaa_houte.aspx imulatio Output aalysis 3/4/06 This lecture Output: A simulatio determies the value of some performace measures, e.g. productio per hour, average queue
More informationArithmetic Circuits. (Part I) Randy H. Katz University of California, Berkeley. Spring Time vs. Space Trade-offs. Arithmetic Logic Units
rithmetic rcuits (art I) Rady H. Katz Uiversity of Califoria, erkeley otivatio rithmetic circuits are excellet examples of comb. logic desig Time vs. pace Trade-offs Doig thigs fast requires more logic
More informationw (1) ˆx w (1) x (1) /ρ and w (2) ˆx w (2) x (2) /ρ.
2 5. Weighted umber of late jobs 5.1. Release dates ad due dates: maximimizig the weight of o-time jobs Oce we add release dates, miimizig the umber of late jobs becomes a sigificatly harder problem. For
More informationMath 155 (Lecture 3)
Math 55 (Lecture 3) September 8, I this lecture, we ll cosider the aswer to oe of the most basic coutig problems i combiatorics Questio How may ways are there to choose a -elemet subset of the set {,,,
More informationClassification of problem & problem solving strategies. classification of time complexities (linear, logarithmic etc)
Classificatio of problem & problem solvig strategies classificatio of time complexities (liear, arithmic etc) Problem subdivisio Divide ad Coquer strategy. Asymptotic otatios, lower boud ad upper boud:
More informationLECTURE 5 PART 2 MOS INVERTERS STATIC DESIGN CMOS. CMOS STATIC PARAMETERS The Inverter Circuit and Operating Regions
LECTURE 5 PART 2 MOS INVERTERS STATIC ESIGN CMOS Objectives for Lecture 5 - Part 2* Uderstad the VTC of a CMOS iverter. Uderstad static aalysis of the CMOS iverter icludig breakpoits, VOL, V OH,, V IH,
More informationAnalytic Continuation
Aalytic Cotiuatio The stadard example of this is give by Example Let h (z) = 1 + z + z 2 + z 3 +... kow to coverge oly for z < 1. I fact h (z) = 1/ (1 z) for such z. Yet H (z) = 1/ (1 z) is defied for
More informationSchool of Mechanical Engineering Purdue University. ME375 Frequency Response - 1
Case Study ME375 Frequecy Respose - Case Study SUPPORT POWER WIRE DROPPERS Electric trai derives power through a patograph, which cotacts the power wire, which is suspeded from a cateary. Durig high-speed
More informationMinimum Dominating Set Approach to Analysis and Control of Biological Networks
Miimum Domiatig Set Approach to Aalysis ad Cotrol of Biological Networks Tatsuya Akutsu Bioiformatics Ceter Istitute for Chemical Research, Kyoto Uiversity Joit work with Jose Nacher i Toho Uiversity Motivatio:
More informationNOTES ON DISTRIBUTIONS
NOTES ON DISTRIBUTIONS MICHAEL N KATEHAKIS Radom Variables Radom variables represet outcomes from radom pheomea They are specified by two objects The rage R of possible values ad the frequecy fx with which
More informationHomework #4 Chapter 17
oework #4 hapter 17 roperties o Solutios 1. a) NO(s) + (aq) + NO - (aq) ) NaSO4(s) Na + (aq) + SO4 - (aq) c) Al(NO)(s) Al + (aq) + NO - (aq) d) SrBr(s) Sr + (aq) + Br - (aq) e) KlO4(s) K + (aq) + lo4 -
More informationELEG3503 Introduction to Digital Signal Processing
ELEG3503 Itroductio to Digital Sigal Processig 1 Itroductio 2 Basics of Sigals ad Systems 3 Fourier aalysis 4 Samplig 5 Liear time-ivariat (LTI) systems 6 z-trasform 7 System Aalysis 8 System Realizatio
More informationOptimization Methods MIT 2.098/6.255/ Final exam
Optimizatio Methods MIT 2.098/6.255/15.093 Fial exam Date Give: December 19th, 2006 P1. [30 pts] Classify the followig statemets as true or false. All aswers must be well-justified, either through a short
More informationChapter 4 : Laplace Transform
4. Itroductio Laplace trasform is a alterative to solve the differetial equatio by the complex frequecy domai ( s = σ + jω), istead of the usual time domai. The DE ca be easily trasformed ito a algebraic
More informationLinear Programming! References! Introduction to Algorithms.! Dasgupta, Papadimitriou, Vazirani. Algorithms.! Cormen, Leiserson, Rivest, and Stein.
Liear Programmig! Refereces! Dasgupta, Papadimitriou, Vazirai. Algorithms.! Corme, Leiserso, Rivest, ad Stei. Itroductio to Algorithms.! Slack form! For each costrait i, defie a oegative slack variable
More informationSOME MULTI-STEP ITERATIVE ALGORITHMS FOR MINIMIZATION OF UNCONSTRAINED NON LINEAR FUNCTIONS
I.J.E.M.S. VOL. : -7 ISS 9-6X SOME MULTI-STEP ITERATIVE ALGORITHMS FOR MIIMIZATIO OF UCOSTRAIED O LIEAR FUCTIOS K.Karthikea S.K.Khadar Babu M.Sudaramurth B.Rajesh Aad School o Advaced Scieces VIT Uiversit
More informationThe Pendulum. Purpose
The Pedulum Purpose To carry out a example illustratig how physics approaches ad solves problems. The example used here is to explore the differet factors that determie the period of motio of a pedulum.
More informationApplications of Distributed Arithmetic to Digital Signal Processing: A Tutorial Review
pplicatios of Distriuted rithmetic to Digital Sigal Processig: Tutorial Review Ref: Staley. White, pplicatios of Distriuted rithmetic to Digital Sigal Processig: Tutorial Review, IEEE SSP Magazie, July,
More informationis also known as the general term of the sequence
Lesso : Sequeces ad Series Outlie Objectives: I ca determie whether a sequece has a patter. I ca determie whether a sequece ca be geeralized to fid a formula for the geeral term i the sequece. I ca determie
More informationNumerical Astrophysics: hydrodynamics
Numerical Astrophysics: hydrodyamics Part 1: Numerical solutios to the Euler Equatios Outlie Numerical eperimets are a valuable tool to study astrophysical objects (where we ca rarely do direct eperimets).
More informationComputational Fluid Dynamics. Lecture 3
Computatioal Fluid Dyamics Lecture 3 Discretizatio Cotiued. A fourth order approximatio to f x ca be foud usig Taylor Series. ( + ) + ( + ) + + ( ) + ( ) = a f x x b f x x c f x d f x x e f x x f x 0 0
More informationArithmetic Circuits. (Part I) Randy H. Katz University of California, Berkeley. Spring 2007
rithmetic Circuits (Part I) Rady H. Katz Uiversity of Califoria, erkeley prig 27 Lecture #23: rithmetic Circuits- Motivatio rithmetic circuits are excellet examples of comb. logic desig Time vs. pace Trade-offs
More informationAdvanced Course of Algorithm Design and Analysis
Differet complexity measures Advaced Course of Algorithm Desig ad Aalysis Asymptotic complexity Big-Oh otatio Properties of O otatio Aalysis of simple algorithms A algorithm may may have differet executio
More informationECEN Microelectronics. Semiconductor Physics and P/N junctions 2/05/19
ECEN 3250 Microelectroics Semicoductor Physics ad P/N juctios 2/05/19 Professor J. Gopiath Professor J. Gopiath Uiversity of Colorado at Boulder Microelectroics Sprig 2014 Overview Eergy bads Atomic eergy
More informationSOLUTIONS: ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 3/27/13) e E i E T
SOUIONS: ECE 606 Homework Week 7 Mark udstrom Purdue Uiversity (revised 3/27/13) 1) Cosider a - type semicoductor for which the oly states i the badgap are door levels (i.e. ( E = E D ). Begi with the
More information3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,
3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [
More informationNotes for Lecture 5. 1 Grover Search. 1.1 The Setting. 1.2 Motivation. Lecture 5 (September 26, 2018)
COS 597A: Quatum Cryptography Lecture 5 (September 6, 08) Lecturer: Mark Zhadry Priceto Uiversity Scribe: Fermi Ma Notes for Lecture 5 Today we ll move o from the slightly cotrived applicatios of quatum
More informationLecture 5: HBT DC Properties. Basic operation of a (Heterojunction) Bipolar Transistor
Lecture 5: HT C Properties asic operatio of a (Heterojuctio) ipolar Trasistor Abrupt ad graded juctios ase curret compoets Quasi-Electric Field Readig Guide: 143-16: 17-177 1 P p ++.53 Ga.47 As.53 Ga.47
More informationSummary of pn-junction (Lec )
Lecture #12 OUTLNE Diode aalysis ad applicatios cotiued The MOFET The MOFET as a cotrolled resistor Pich-off ad curret saturatio Chael-legth modulatio Velocity saturatio i a short-chael MOFET Readig Howe
More informationFFTs in Graphics and Vision. The Fast Fourier Transform
FFTs i Graphics ad Visio The Fast Fourier Trasform 1 Outlie The FFT Algorithm Applicatios i 1D Multi-Dimesioal FFTs More Applicatios Real FFTs 2 Computatioal Complexity To compute the movig dot-product
More informationLecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting
Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would
More informationState space systems analysis
State pace ytem aalyi Repreetatio of a ytem i tate-pace (tate-pace model of a ytem To itroduce the tate pace formalim let u tart with a eample i which the ytem i dicuio i a imple electrical circuit with
More informationLecture 9: Diffusion, Electrostatics review, and Capacitors. Context
EECS 5 Sprig 4, Lecture 9 Lecture 9: Diffusio, Electrostatics review, ad Capacitors EECS 5 Sprig 4, Lecture 9 Cotext I the last lecture, we looked at the carriers i a eutral semicoductor, ad drift currets
More informationFinite Automata. Reading: Chapter 2
Fiite Automata Readig: Chapter 2 Fiite Automato (FA) Iformally, a state diagram that comprehesively captures all possible states ad trasitios that a machie ca take while respodig to a stream or sequece
More information6.867 Machine learning
6.867 Machie learig Mid-term exam October, ( poits) Your ame ad MIT ID: Problem We are iterested here i a particular -dimesioal liear regressio problem. The dataset correspodig to this problem has examples
More information1. pn junction under bias 2. I-Vcharacteristics
Lecture 10 The p Juctio (II) 1 Cotets 1. p juctio uder bias 2. I-Vcharacteristics 2 Key questios Why does the p juctio diode exhibit curret rectificatio? Why does the juctio curret i forward bias icrease
More informationStatistical Pattern Recognition
Statistical Patter Recogitio Classificatio: No-Parametric Modelig Hamid R. Rabiee Jafar Muhammadi Sprig 2014 http://ce.sharif.edu/courses/92-93/2/ce725-2/ Ageda Parametric Modelig No-Parametric Modelig
More informationECE594I Notes set 13: Two-port Noise Parameters
C594 otes, M. Rodwell, copyrighted C594 Notes set 13: Two-port Noise Parameters Mark Rodwell Uiversity of Califoria, Sata Barbara rodwell@ece.ucsb.edu 805-893-3244, 805-893-3262 fax Refereces ad Citatios:
More information1 Hash tables. 1.1 Implementation
Lecture 8 Hash Tables, Uiversal Hash Fuctios, Balls ad Bis Scribes: Luke Johsto, Moses Charikar, G. Valiat Date: Oct 18, 2017 Adapted From Virgiia Williams lecture otes 1 Hash tables A hash table is a
More informationu t u 0 ( 7) Intuitively, the maximum principles can be explained by the following observation. Recall
Oct. Heat Equatio M aximum priciple I thi lecture we will dicu the maximum priciple ad uiquee of olutio for the heat equatio.. Maximum priciple. The heat equatio alo ejoy maximum priciple a the Laplace
More informationTime-Domain Representations of LTI Systems
2.1 Itroductio Objectives: 1. Impulse resposes of LTI systems 2. Liear costat-coefficiets differetial or differece equatios of LTI systems 3. Bloc diagram represetatios of LTI systems 4. State-variable
More informationLecture 5. Random variable and distribution of probability
Itroductio to theory of probability ad statistics Lecture 5. Radom variable ad distributio of probability prof. dr hab.iż. Katarzya Zarzewsa Katedra Eletroii, AGH e-mail: za@agh.edu.pl http://home.agh.edu.pl/~za
More informationSequences, Mathematical Induction, and Recursion. CSE 2353 Discrete Computational Structures Spring 2018
CSE 353 Discrete Computatioal Structures Sprig 08 Sequeces, Mathematical Iductio, ad Recursio (Chapter 5, Epp) Note: some course slides adopted from publisher-provided material Overview May mathematical
More informationSolutions - Homework # 1
ECE-4: Sigals ad Systems Summer Solutios - Homework # PROBLEM A cotiuous time sigal is show i the figure. Carefully sketch each of the followig sigals: x(t) a) x(t-) b) x(-t) c) x(t+) d) x( - t/) e) x(t)*(
More informationAppendix: The Laplace Transform
Appedix: The Laplace Trasform The Laplace trasform is a powerful method that ca be used to solve differetial equatio, ad other mathematical problems. Its stregth lies i the fact that it allows the trasformatio
More informationLecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting
Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would
More informationGrowth of Functions. Chapter 3. CPTR 430 Algorithms Growth of Functions 1
Growth o Fuctios Chapter 3 CPTR 430 Alorithms Growth o Fuctios 1 Asymptotic Eiciecy o Alorithms Idea: Look at iput sizes lare eouh to make rui time order o rowth relevat How does the rui time o a alorithm
More informationReal Variables II Homework Set #5
Real Variables II Homework Set #5 Name: Due Friday /0 by 4pm (at GOS-4) Istructios: () Attach this page to the frot of your homework assigmet you tur i (or write each problem before your solutio). () Please
More information