APPLICATION NOTE UNDERSTANDING EFFECTIVE BITS
|
|
- Gwen Walters
- 5 years ago
- Views:
Transcription
1 APPLICATION NOTE AN95091 INTRODUCTION UNDERSTANDING EFFECTIVE BITS Toy Girard, Sigatec, Desig ad Applicatios Egieer Oe criteria ofte used to evaluate a Aalog to Digital Coverter (ADC) or data acquisitio system is the effective umber of bits achieved. The effective umber of bits provides a meas to evaluate the overall performace of a system. However, like ay other parameter, a uderstadig of the theory behid the effective bits, ad differet methods used to determie effective bits is ecessary to properly compare compoets ad systems. The itet of this applicatio ote is to provide the basic theory behid effective bits, describe differet methods used to determie effective bits, ad to explai the limitatios i its usage. NUMBER OF BITS VERSES EFFECTIVE BITS The umber of bits i a data acquisitio system is ormally specified as the umber of bits of the digitizer. Ay data acquisitio system, or ADC, has iheret performace limitatios. Whe evaluatig a acquisitio system the effective umber of bits provided by the system ca useful i determiig if the system is right for the applicatio. There are may sources of error i a acquisitio system. Cosiderig a system i terms of effective bits, all error sources are icluded. Evaluatio of system performace is made without the eed to cosider the idividual error sources, all of which may ot be characterized by the maufacturer. THE PERFECT SYSTEM A perfect data acquisitio system is oe i which the captured aalog sigal is free from oise ad distortio. The system is free from ay frequecy depedet performace characteristics, up to the maximum samplig rate ad the badwidth limit of the system. I this system the oly limitatio to system performace would be the quatizatio error iheret i all samplig systems. Quatizatio error occurs because a aalog sigal is sampled ad its level represeted by a fiite umber. The output of a ADC has 2 levels, where is the umber of coverter bits. For example, a 8 bit ADC has 2 8, or 256 levels. The bit which represets the smallest voltage chage is called the least sigificat bit (lsb). Each sample has a quatizatio error of up to ±0.5 of the lsb due to the differece betwee the true aalog voltage level ad the level represeted by the ADC output. 1
2 The quatizatio error defies a base lie oise level which limits the systems ability to resolve small sigals i a perfect system. This is commoly referred to as Sigal to Noise ratio (S/N) which is the ratio of the Root Mea Square (RMS) of the largest sigal divided by the RMS value of the oise. The maximum sigal level is 2 bits ad the oise is 1 bit. The higher the resolutio of a system, the larger the maximum sigal level with respect to the 1 bit quatizatio oise. The result is that higher resolutio systems have a lower base lie oise level resultig i a greater dyamic rage. The SNR of a ideal system S is foud usig the maximum RMS sigal level N ideal (V RMS ) ad the quatizatio error ( QE RMS ). The mea square of the quatizatio error is foud by itegratig over the quatizatio voltage error rage as follows: QE MS + V / 2 q E V de V q = = 12 V / 2 q 2 2 q The RMS value of the quatizatio error is foud by takig the square root of the mea square error: QE RMS 2 Vq Vq = = where V q is the quaitizatio voltage ad is equal to 1 bit. The ideal sigal to oise ratio ca the be foud as follows: V RMS = QE RMS = S VRMS = = = = N ideal QE 1 RMS I terms of decibels: S 20 log 10 ( ) db N ideal or S N ideal ( ) db where is the umber of bits. 2
3 THE REAL SYSTEM No system is ideal. Every coverter has o-liearity, oise from referece voltages, ad aperture jitter. Every system adds oise to the aalog sigal beig sampled, creates sigal distortio (harmoics), ad has some amout of clock jitter. All these elemets, ad more, cotribute to system performace degradatio with respect to the ideal system. I effect, all error sources combie to limit the effective resolutio of a system. Because differet error sources are depedet upo various operatig coditios, the effective umber of bits is also depedet upo the operatig coditios. The amplitude of the test sigal ca chage the level of distortio. Sigal amplitudes ear full scale should ormally be used. Typically the frequecy of the samplig clock has little affect o the effective umber of bits. The geerally accepted method is to use the systems maximum samplig frequecy for effective bits characterizatio. The frequecy ad amplitude of the iput aalog sigal have the largest affect o the effective umber of bits. This is geerally due both to distortio of the sigal by the aalog frot ed ad the system oise icrease due to clock jitter as the sigal frequecy is icreased. I state-of-the-art systems i terms of samplig rate ad aalog badwidth, the effective umber of bits geerally decreases sigificatly as the sigal frequecy icreases. SYSTEM PERFORMANCE MEASUREMENTS The effective umber of bits is determied by samplig a spectrally pure siusoidal wave ad determiig the RMS sigal ad oise levels recorded by the system. I this case oise refers to aythig which is ot sigal, this icludes quatizatio oise, oise from the iput sigal, ad ay distortio of the sigal. Ofte data acquisitio system maufacturers specify a performace parameter called SINAD. SINAD is the ratio of the fudametal SINusoidal sigal power acquired to the total Noise Ad Distortio. Because this parameter cotais oise ad distortio, it ca be used directly to calculate effective bits. Whe Sigal to Noise Ratio (SNR) is specified, it is ofte the ratio of the fudametal siusoidal sigal power to the oise, ot icludig the harmoics. Figure 1 shows the relatioship of SINAD to SNR i a typical applicatio. Usig SNR to calculate the effective bits of a system is acceptable i some applicatios. For example a commuicatios system where the badwidth of iterest is small ad it is kow that o harmoics, icludig those above the Nyquist limit which will be aliased, will fall withi that bad. 3
4 db DATA ANALYSIS SINAD VS SNR Sigal SINAD SNR FIGURE 1 There are two data aalysis methods used to determie SINAD, ad therefore effective bits. Oe method uses time domai data aalysis ad the other uses frequecy domai data aalysis. Time domai aalysis uses a complex algorithm to fit a perfect sie curve to the acquired time domai data poits. The algorithm must match the sie-wave frequecy, phase, amplitude, ad offset to the data. The perfect wave is the subtracted from the data ad the remaiig data is oise ad distortio. This is the method commoly used by some ADC maufacturers. Frequecy domai aalysis uses a FFT to covert time domai data to the frequecy domai. The appropriate FFT frequecy bis are the selected to determie SINAD. Sigatec, ad some ADC maufacturers, use the frequecy domai aalysis method. Sigatec uses a 4096 poit FFT with a Blackma-Harris widow to covert the data to the frequecy domai. The eergy from a sigal spreads over a umber of bis i the FFT. This makes selectio of bis for sigal calculatios importat whe usig the frequecy domai method. A improper bi selectio will affect the SINAD/effective bits calculatio. Usig a umber of frequecy bis which is greater tha the umber which actually cotai sigal eergy will result i summig oise eergy ito the sigal, resultig i a erroeously high sigal level. Usig too few frequecy bis to represet the fudametal will result i a fudametal power which is too low ad a oise level which is too high. The first 4 bis of the FFT represet the dc term caused by offset shift ad the FFT widowig fuctio, ad are excluded from aalysis. The 9 bis cetered 4
5 aroud the peak frequecy are summed to determie the fudametal sigal power ad the remaiig bis are cosidered oise for the SINAD calculatio. Figures 2, 4, ad 6 show the frequecy domai plots of data acquired with Sigatec s DA500A, 500MHz digitizig rate, 500MHz aalog badwidth data acquisitio system. Figures 3, 5, ad 7 are exploded views of showig the frequecy bis at the fudametal frequecy. The shaded bis are the oes used to calculate the level of the fudametal frequecy. Amplitude (db) FFT RESULT (25MHz) FIGURE 2 FFT BINS (25MHz) FIGURE 3 Amplitude (db) FFT RESULT (95MHz) FIGURE 4 FFT BINS (95MHz) FIGURE 5 Amplitude (db) FFT RESULT (230MHz) FIGURE 6 FFT BINS (230MHz) FIGURE 7 5
6 The selectio of the frequecy used for SINAD ad effective bits test is importat. The sigal frequecy must be selected such that the harmoic terms are sufficietly separated from the fudametal so as ot to be cosidered part of the sigal. The relatioship of the sigal frequecy to the samplig frequecy must be selected such that the harmoics, which may be above the Nyquist limit, do ot alias oto the fudametal. This would cause the harmoic eergy to sum with the sigal eergy resultig i a erroeously high sigal level ad a lower oise level. The resultig effective bits value is sigificatly better tha the system actually provides. Figures 8 ad 9 illustrate the importace of frequecy selectio. The fudametal frequecy is 166.4MHz. This results i a 2d harmoic of 332.8MHz which is above the Nyquist limit, so it will alias to 167.2MHz. If the fudametal frequecy was slightly higher, the 2d harmoic will fold directly o top of the fudametal. Amplitude (db) FFT RESULT (166.4MHz) FIGURE FFT BINS (166.4MHz) Fudametal 2d Harmoic FIGURE 9 Whe values for SINAD are icluded i product specificatios, a simple calculatio yields the effective umber of bits. The equatio S ( ) db was N ideal previously show to represet the ideal Sigal to Noise ratio, assumig a full scale iput sigal, ad a oise value which icludes distortio. This equatio ca be used for a S effective bits calculatio by replacig the theoretical with the measured SINAD N ideal ad lettig equal the effective umber of bits rather tha the actual digitizer bits. Solvig this equatio for effective bits yields: EffectiveBits = SINAD where SINAD is give i db ad the test sigal for SINAD is ear full scale. 6
7 Figure 10 shows the effective bits whe usig SINAD ad SNR for the calculatio. The decrease i effective bits as the sigal frequecy icreases is typical of high speed, high badwidth systems. The decrease i effective bits from the SNR calculatio, labeled A i Figure 10, is due to digitizer clock ad aperture jitter. The differece i the decrease betwee the SNR ad the SINAD effective bits, labeled B i Figure 10 is due to sigal distortio. 7 EFFECTIVE BITS Number Eff. Bits A B SINAD SNR FIGURE 10 Some maufactures add a correctio factor to the SINAD term whe calculatig effective bits to correct for the differece i dyamic rage betwee the amplitude of the test sigal ad the maximum full scale amplitude of the coverter. I a high speed, large badwidth system addig this correctio factor is iappropriate. The ature of the correctio i the calculatio assumes that uused dyamic rage would be pure sigal with o oise or distortio. I real life high speed systems this will ot occur ad the calculatio will yield a ufairly large effective umber of bits. For these reasos Sigatec does ot iclude this correctio factor i ay calculatios or graphs give i this documet. DROPPING BITS A commo miscoceptio regardig effective bits ad system performace is that ay resolutio beyod the effective bits is useless. For example, i a 8 bit system with 6 effective bits, the 2 least sigificat bits are useless ad ca be disregarded i data aalysis. This is ot true. As discussed above, the effective umber of bits, or SINAD, represets the overall system performace. I other words, these parameters are the combiatio of all error sources. If the total error is broke ito two parts, quatizatio error ad all other errors, the total system oise is give by: 7
8 Error = E + E 2 2 q s where E q is the quatizatio error ad E s is the RMS values of all other errors. Usig a digitizer with fewer bits, or droppig the bits from processig icreases the quatizatio error. The equatio above shows that as the quatizatio error icreases, the overall error icreases, icreasig SINAD ad decreasig the effective umber of bits. If the oise due to system oise ad error is ot sigificatly greater tha quatizatio error, the removig bits from the data will icrease the overall oise level, which reduces data quality. Figure 11 shows data which was acquired with Sigatec s DA500A data acquisitio board. The graph shows four SINAD curves, oe each for data acquired with 8, 7, 6, ad 5 digitizer bits. The y-axis grid lies are positioed at the SINAD values correspodig to a perfect 8, 7, 6, 5, ad 4 bit system. At low frequecies where the errors itroduced by the system are small relative to the quatizatio error, each of the trucated data sets closely matches its respective effective bit value. However, at higher frequecies where the sigal error icreases, there is a decrease i the SINAD value. 48 SINAD WITH TRUNCATED BITS 42 db Bits 7 Bits 6 Bits 5 Bits FIGURE 11 8
9 EVALUATING RESULTS As previously stated, the effective umber of bits achieved by a data acquisitio system is a reflectio of the systems overall performace. Evaluatio of a system s effective bits show that if a applicatio requires a sigal to be resolved to true eight bits of resolutio, for example, the a digitizer with a resolutio higher tha eight bits is required. Whe usig effective bits to evaluate system performace, the method used to determie the umber is importat. The method must allow for the iclusio or exclusio of various parameters depedig o the specifics of the applicatio. For example SINAD, which icludes distortio terms, should ormally be used to derive effective bits, but i some applicatios usig SNR may be appropriate. It is also importat to evaluate the effective bits at a frequecy ad amplitude appropriate for the applicatio. The effective bits, ad other performace parameters, should be specified at a particular frequecy or set of frequecies. This is importat due the ormal decrease i performace as the sigal frequecy icreases i high performace systems. The effective umber of bits for a high performace system caot be assumed to be the same as the effective umber of bits for the ADC used i the system. Therefore the effective umber of bits, alog with all other performace parameters must be specified for the etire system. Referecig ADC maufactures specificatios i system data sheets provides iformatio which is ot useful to the system user. Whe evaluatig a system for a particular applicatio it is ofte ecessary to look beyod the effective bits parameter. While the effective umber of bits gives a idicatio of overall system performace, it may ot be the best parameter to use whe cosiderig a system for a particular applicatio. Other parameters such as Spurious Free Dyamic Rage (SFDR) or Total Harmoic Distortio (THD) are more appropriate for some applicatios. Ofte it is importat to evaluate characteristics such as harmoic distortio or SNR as a fuctio of sigal frequecy. SUMMARY The effective umber of bits achieved by a data acquisitio system ca provide a user with a overall isight ito the systems performace. However, as with ay other performace parameters, the user should uderstad the methods used by the maufacturer to determie the effective umber of bits. I critical applicatios it is geerally ecessary to look beyod the umber effective bits to other performace specificatios which idetify specific system limitatios. 9
Objectives. Some Basic Terms. Analog and Digital Signals. Analog-to-digital conversion. Parameters of ADC process: Related terms
Objectives. A brief review of some basic, related terms 2. Aalog to digital coversio 3. Amplitude resolutio 4. Temporal resolutio 5. Measuremet error Some Basic Terms Error differece betwee a computed
More informationSampling. Introduction to Digital Data Acquisition: Physical world is analog CSE/EE Digital systems need to
Itroductio to Digital Data Acuisitio: Samplig Physical world is aalog Digital systems eed to Measure aalog uatities Switch iputs, speech waveforms, etc Cotrol aalog systems Computer moitors, automotive
More informationMeasurement of Equivalent Input Distortion AN 20
Measuremet of Equivalet Iput Distortio AN 2 Applicatio Note to the R&D SYSTEM Traditioal measuremets of harmoic distortio performed o loudspeakers reveal ot oly the symptoms of the oliearities but also
More informationSingle Bit DACs in a Nutshell. Part I DAC Basics
Sigle Bit DACs i a Nutshell Part I DAC Basics By Dave Va Ess, Pricipal Applicatio Egieer, Cypress Semicoductor May embedded applicatios require geeratig aalog outputs uder digital cotrol. It may be a DC
More informationX-Bar and S-Squared Charts
STATGRAPHICS Rev. 7/4/009 X-Bar ad S-Squared Charts Summary The X-Bar ad S-Squared Charts procedure creates cotrol charts for a sigle umeric variable where the data have bee collected i subgroups. It creates
More informationA Novel Small Signal Power Line Quality Measurement System
IMTC 3 - Istrumetatio ad Measuremet Techology Coferece Vail, CO, USA, - May 3 A ovel Small Sigal Power Lie Quality Measuremet System Paul B. Crilly, Erik Leadro Boaldi, Levy Ely de Lacarda de Oliveira,
More information4. INTERSYMBOL INTERFERENCE
DATA COMMUNICATIONS 59 4. INTERSYMBOL INTERFERENCE 4.1 OBJECT The effects of restricted badwidth i basebad data trasmissio will be studied. Measuremets relative to itersymbol iterferece, usig the eye patter
More informationINCREASE OF STRAIN GAGE OUTPUT VOLTAGE SIGNALS ACCURACY USING VIRTUAL INSTRUMENT WITH HARMONIC EXCITATION
XIX IMEKO World Cogress Fudametal ad Applied Metrology September 6, 9, Lisbo, Portugal INCREASE OF STRAIN GAGE OUTPUT VOLTAGE SIGNALS ACCURACY USING VIRTUAL INSTRUMENT WITH HARMONIC EXCITATION Dalibor
More informationECE 333: Introduction to Communication Networks Fall Lecture 4: Physical layer II
ECE 333: Itroductio to Commuicatio Networks Fall 22 Lecture : Physical layer II Impairmets - distortio, oise Fudametal limits Examples Notes: his lecture cotiues the discussio of the physical layer. Recall,
More informationAnalysis of SDR GNSS Using MATLAB
Iteratioal Joural of Computer Techology ad Electroics Egieerig (IJCTEE) Volume 5, Issue 3, Jue 2015 Aalysis of SDR GNSS Usig MATLAB Abstract This paper explais a software defied radio global avigatio satellite
More informationBy: Pinank Shah. Date : 03/22/2006
By: Piak Shah Date : 03/22/2006 What is Strai? What is Strai Gauge? Operatio of Strai Gauge Grid Patters Strai Gauge Istallatio Wheatstoe bridge Istrumetatio Amplifier Embedded system ad Strai Gauge Strai
More informationE X P E R I M E N T 13
E X P E R I M E N T 13 Stadig Waves o a Strig Produced by the Physics Staff at Colli College Copyright Colli College Physics Departmet. All Rights Reserved. Uiversity Physics, Exp 13: Stadig Waves o a
More informationEncode Decode Sample Quantize [ ] [ ]
Referece Audio Sigal Processig I Shyh-Kag Jeg Departmet of Electrical Egieerig/ Graduate Istitute of Commuicatio Egieerig M. Bosi ad R. E. Goldberg, Itroductio to Digital Audio Codig ad Stadards, Kluwer
More informationCAEN Tools for Discovery
Applicatio Note AN2506 Digital Gamma Neutro discrimiatio with Liquid Scitillators Viareggio 19 November 2012 Itroductio I recet years CAEN has developed a complete family of digitizers that cosists of
More informationProblem of calculating time delay between pulse arrivals
America Joural of Egieerig Research (AJER) 5 America Joural of Egieerig Research (AJER) e-issn: 3-847 p-issn : 3-936 Volume-4, Issue-4, pp-3-4 www.ajer.org Research Paper Problem of calculatig time delay
More informationCHAPTER 5 A NEAR-LOSSLESS RUN-LENGTH CODER
95 CHAPTER 5 A NEAR-LOSSLESS RUN-LENGTH CODER 5.1 GENERAL Ru-legth codig is a lossless image compressio techique, which produces modest compressio ratios. Oe way of icreasig the compressio ratio of a ru-legth
More informationCascaded Feedforward Sigma-delta Modulator for Wide Bandwidth Applications
Tamkag Joural of Sciece ad Egieerig, Vol. 4, No., pp. 55-64 () 55 Cascaded Feedforward Sigma-delta Modulator for Wide Badwidth Applicatios Je-Shiu Chiag, Teg-Hug Chag ad Pou-Chu Chou Departmet of Electrical
More informationLINEAR-PHASE FIR FILTERS: THE WINDOWING METHOD
LINEAR-PHASE FIR FILTERS: THE WINDOWING ETHOD Prof. Siripog Potisuk FIR Filter Characteristics Completely specified by iput-output relatio: y[ ] b k0 x[ k] b k = filter coefficiets ad +1 = filter legth
More informationOutline. Motivation. Analog Functional Testing in Mixed-Signal Systems. Motivation and Background. Built-In Self-Test Architecture
Aalog Fuctioal Testig i Mixed-Sigal s Jie Qi Dept. of Electrical & Computer Egieerig Aubur Uiversity Co-Advisors: Charles Stroud ad Foster Dai Outlie Motivatio ad Backgroud Built-I Self-Test Architecture
More informationThe Institute of Chartered Accountants of Sri Lanka
The Istitute of Chartered Accoutats of Sri Laka Postgraduate Diploma i Busiess ad Fiace Quatitative Techiques for Busiess Hadout 02:Presetatio ad Aalysis of data Presetatio of Data The Stem ad Leaf Display
More informationPRACTICAL FILTER DESIGN & IMPLEMENTATION LAB
1 of 7 PRACTICAL FILTER DESIGN & IMPLEMENTATION LAB BEFORE YOU BEGIN PREREQUISITE LABS Itroductio to Oscilloscope Itroductio to Arbitrary/Fuctio Geerator EXPECTED KNOWLEDGE Uderstadig of LTI systems. Laplace
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 3 Sigals & Systems Prof. Mark Fowler Note Set #6 D-T Systems: DTFT Aalysis of DT Systems Readig Assigmet: Sectios 5.5 & 5.6 of Kame ad Heck / Course Flow Diagram The arrows here show coceptual flow
More informationCh 9 Sequences, Series, and Probability
Ch 9 Sequeces, Series, ad Probability Have you ever bee to a casio ad played blackjack? It is the oly game i the casio that you ca wi based o the Law of large umbers. I the early 1990s a group of math
More informationGENERATE AND MEASURE STANDING SOUND WAVES IN KUNDT S TUBE.
Acoustics Wavelegth ad speed of soud Speed of Soud i Air GENERATE AND MEASURE STANDING SOUND WAVES IN KUNDT S TUBE. Geerate stadig waves i Kudt s tube with both eds closed off. Measure the fudametal frequecy
More informationThe Eye. Objectives: Introduction. PHY 192 The Eye 1
PHY 92 The Eye The Eye Objectives: Describe the basic process of image formatio by the huma eye ad how it ca be simulated i the laboratory. Kow what measuremets are ecessary to quatitatively diagose ear-sightedess
More informationIntroduction to Wireless Communication Systems ECE 476/ECE 501C/CS 513 Winter 2003
troductio to Wireless Commuicatio ystems ECE 476/ECE 501C/C 513 Witer 2003 eview for Exam #1 March 4, 2003 Exam Details Must follow seatig chart - Posted 30 miutes before exam. Cheatig will be treated
More informationMethods to Reduce Arc-Flash Hazards
Methods to Reduce Arc-Flash Hazards Exercise: Implemetig Istataeous Settigs for a Maiteace Mode Scheme Below is a oe-lie diagram of a substatio with a mai ad two feeders. Because there is virtually o differece
More informationPRACTICAL ANALOG DESIGN TECHNIQUES
PRACTICAL ANALOG DESIGN TECHNIQUES SINGLE-SUPPLY AMPLIFIERS HIGH SPEED OP AMPS HIGH RESOLUTION SIGNAL CONDITIONING ADCs HIGH SPEED SAMPLING ADCs UNDERSAMPLING APPLICATIONS MULTICHANNEL APPLICATIONS OVERVOLTAGE
More informationAC : USING ELLIPTIC INTEGRALS AND FUNCTIONS TO STUDY LARGE-AMPLITUDE OSCILLATIONS OF A PENDULUM
AC 007-7: USING ELLIPTIC INTEGRALS AND FUNCTIONS TO STUDY LARGE-AMPLITUDE OSCILLATIONS OF A PENDULUM Josue Njock-Libii, Idiaa Uiversity-Purdue Uiversity-Fort Waye Josué Njock Libii is Associate Professor
More informationA New Space-Repetition Code Based on One Bit Feedback Compared to Alamouti Space-Time Code
Proceedigs of the 4th WSEAS It. Coferece o Electromagetics, Wireless ad Optical Commuicatios, Veice, Italy, November 0-, 006 107 A New Space-Repetitio Code Based o Oe Bit Feedback Compared to Alamouti
More informationMassachusetts Institute of Technology Dept. of Electrical Engineering and Computer Science Fall Semester, Introduction to EECS 2.
Massachusetts Istitute of Techology Dept. of Electrical Egieerig ad Computer Sciece Fall Semester, 006 6.08 Itroductio to EECS Prelab Exercises Pre-Lab#3 Modulatio, demodulatio, ad filterig are itegral
More informationDelta- Sigma Modulator with Signal Dependant Feedback Gain
Delta- Sigma Modulator with Sigal Depedat Feedback Gai K.Diwakar #1 ad V.Vioth Kumar *2 # Departmet of Electroics ad Commuicatio Egieerig * Departmet of Electroics ad Istrumetatio Egieerig Vel Tech Uiversity,Cheai,
More information(2) The MOSFET. Review of. Learning Outcome. (Metal-Oxide-Semiconductor Field Effect Transistor) 2.0) Field Effect Transistor (FET)
EEEB73 Electroics Aalysis & esig II () Review of The MOSFET (Metal-Oxide-Semicoductor Field Effect Trasistor) Referece: Neame, Chapter 3 ad Chapter 4 Learig Outcome Able to describe ad use the followig:
More informationIntermediate Information Structures
Modified from Maria s lectures CPSC 335 Itermediate Iformatio Structures LECTURE 11 Compressio ad Huffma Codig Jo Roke Computer Sciece Uiversity of Calgary Caada Lecture Overview Codes ad Optimal Codes
More informationLecture 28: MOSFET as an Amplifier. Small-Signal Equivalent Circuit Models.
hites, EE 320 ecture 28 Page 1 of 7 ecture 28: MOSFET as a Amplifier. Small-Sigal Equivalet Circuit Models. As with the BJT, we ca use MOSFETs as AC small-sigal amplifiers. A example is the so-called coceptual
More informationLaboratory Exercise 3: Dynamic System Response Laboratory Handout AME 250: Fundamentals of Measurements and Data Analysis
Laboratory Exercise 3: Dyamic System Respose Laboratory Hadout AME 50: Fudametals of Measuremets ad Data Aalysis Prepared by: Matthew Beigto Date exercises to be performed: Deliverables: Part I 1) Usig
More informationNOISE IN A SPECTRUM ANALYZER. Carlo F.M. Carobbi and Fabio Ferrini Department of Information Engineering University of Florence, Italy
NOISE IN A SPECTRUM ANALYZER by Carlo.M. Carobbi ad abio errii Departet of Iforatio Egieerig Uiversity of lorece, Italy 1. OBJECTIVE The objective is to easure the oise figure of a spectru aalyzer with
More informationApplication of Improved Genetic Algorithm to Two-side Assembly Line Balancing
206 3 rd Iteratioal Coferece o Mechaical, Idustrial, ad Maufacturig Egieerig (MIME 206) ISBN: 978--60595-33-7 Applicatio of Improved Geetic Algorithm to Two-side Assembly Lie Balacig Ximi Zhag, Qia Wag,
More informationx y z HD(x, y) + HD(y, z) HD(x, z)
Massachusetts Istitute of Techology Departmet of Electrical Egieerig ad Computer Sciece 6.02 Solutios to Chapter 5 Updated: February 16, 2012 Please sed iformatio about errors or omissios to hari; questios
More informationLecture 4: Frequency Reuse Concepts
EE 499: Wireless & Mobile Commuicatios (8) Lecture 4: Frequecy euse Cocepts Distace betwee Co-Chael Cell Ceters Kowig the relatio betwee,, ad, we ca easily fid distace betwee the ceter poits of two co
More informationH2 Mathematics Pure Mathematics Section A Comprehensive Checklist of Concepts and Skills by Mr Wee Wen Shih. Visit: wenshih.wordpress.
H2 Mathematics Pure Mathematics Sectio A Comprehesive Checklist of Cocepts ad Skills by Mr Wee We Shih Visit: weshih.wordpress.com Updated: Ja 2010 Syllabus topic 1: Fuctios ad graphs 1.1 Checklist o Fuctios
More informationHOW BAD RECEIVER COORDINATES CAN AFFECT GPS TIMING
HOW BAD RECEIVER COORDINATES CAN AFFECT GPS TIMING H. Chadsey U.S. Naval Observatory Washigto, D.C. 2392 Abstract May sources of error are possible whe GPS is used for time comparisos. Some of these mo
More informationFLEXIBLE ADC: A DITHER AND OVERSAMPLING BASED SOLUTION TO IMPROVE THE PERFORMANCE OF ADC SYSTEMS
FLEXIBLE : A DITHER AND OVERSAMPLING BASED SOLUTION TO IMPROVE THE PERFORMANCE OF SYSTEMS J.M. Dias Pereira (1), A. Cruz Serra () ad P. Girão () (1) DSI, Escola Superior de Tecologia, Istituto Politécico
More informationSPARQ Dynamic Range Peter J. Pupalaikis VP & Principal Technologist
SPARQ Dyamic Rage Peter J. Pupalaiis VP & Pricipal Techologist Summary This paper discusses the dyamic rage of the SPARQ sigal itegrity etwor aalyzer ad cosiders the impact of several ey specificatios.
More informationResolution. Learning Objectives. What are the four types of resolution?
Ladsat ETM+ image Resolutio Learig Objectives Be able to ame ad defie the four types of data resolutio. Be able to calculate the umber of pixels i a give area. Uderstad the trade-offs betwee differet types
More informationEstimation of reflection location by the correlation coefficient function
Acoustics 8 Paris Estimatio of reflectio locatio by the correlatio coefficiet fuctio H. Shibayama a, T. Araya b, Y. Maabe b ad E. Oarura b a Shibaura Istitute of Techology, 3-7-5, Toyosu, Koto-u, 35-8548
More informationEmbedded Microcomputer Systems Lecture 9.1
Embedded Microcomputer Systems Lecture 9. Recap from last time Aalog circuit desig Noise Microphoe iterface Objectives Active low pass filter Nyquist Theorem ad aliasig Speaker amplifier Lookig at oise,
More informationDelta- Sigma Modulator based Discrete Data Multiplier with Digital Output
K.Diwakar et al. / Iteratioal Joural of Egieerig ad echology (IJE Delta- Sigma Mulator based Discrete Data Multiplier with Digital Output K.Diwakar #,.ioth Kumar *2, B.Aitha #3, K.Kalaiarasa #4 # Departmet
More informationVoice Command Recognition System Based on MFCC and VQ Algorithms
Voice Commad Recogitio System Based o MFCC ad VQ Algorithms Mahdi Shaeh, ad Azizollah Taheri Abstract The goal of this project is to desig a system to recogitio voice commads. Most of voice recogitio systems
More informationA Bipolar Cockcroft-Walton Voltage Multiplier for Gas Lasers
America Joural of Applied cieces 4 (10): 79-799, 007 N 1546-99 007 ciece Publicatios orrespodig Author: A Bipolar ockcroft-walto Voltage Multiplier for Gas Lasers hahid qbal ad Rosli Besar Faculty of Egieerig
More informationComparison of Frequency Offset Estimation Methods for OFDM Burst Transmission in the Selective Fading Channels
Compariso of Frequecy Offset Estimatio Methods for OFDM Burst Trasmissio i the Selective Fadig Chaels Zbigiew Długaszewski Istitute of Electroics ad Telecommuicatios Pozań Uiversity of Techology 60-965
More informationA New FDTD Method for the Study of MRI Pulsed Field Gradient- Induced Fields in the Human Body
A New FDTD Method for the Study of MRI Pulsed Field Gradiet- Iduced Fields i the Huma Body Stuart Crozier, Huawei Zhao ad Liu Feg Cetre For Magetic Resoace, The Uiversity of Queeslad, St. Lucia, Qld 4072,
More informationDesign of FPGA- Based SPWM Single Phase Full-Bridge Inverter
Desig of FPGA- Based SPWM Sigle Phase Full-Bridge Iverter Afarulrazi Abu Bakar 1, *,Md Zarafi Ahmad 1 ad Farrah Salwai Abdullah 1 1 Faculty of Electrical ad Electroic Egieerig, UTHM *Email:afarul@uthm.edu.my
More informationDesign Considerations for Direct RF Sampling Receiver in GNSS Environment
Desig Cosideratios for Direct RF Samplig Receiver i GNSS Eviromet Ville Syrjälä, Mikko Valkama ad Markku Refors Tampere Uiversity of Techology Istitute of Commuicatios Egieerig Korkeakoulukatu 1, Tampere,
More informationECC Recommendation (14)02
ECC Recommedatio (14)02 Protectio of fixed moitorig statios agaist iterferece from earby or strog trasmitters Approved 07 February 2014 ECC/REC/(14)02 Page 2 INTRODUCTION The icreasig use of broadbad moitorig
More informationLogarithms APPENDIX IV. 265 Appendix
APPENDIX IV Logarithms Sometimes, a umerical expressio may ivolve multiplicatio, divisio or ratioal powers of large umbers. For such calculatios, logarithms are very useful. They help us i makig difficult
More informationRoberto s Notes on Infinite Series Chapter 1: Series Section 2. Infinite series
Roberto s Notes o Ifiite Series Chapter : Series Sectio Ifiite series What you eed to ow already: What sequeces are. Basic termiology ad otatio for sequeces. What you ca lear here: What a ifiite series
More informationMid-level representations for audio content analysis *Slides for this lecture were created by Anssi Klapuri
Mid-level represetatios for audio cotet aalysis *Slides for this lecture were created by Assi Klapuri Represetatios 1 Sources: Ellis, Rosethal, Mid-level represetatios for Computatioal Auditory Scee Aalysis,
More informationModelig the Curret Profile Switchig capacitace is oe of the factors that determie dyamic power cosumptio. Power estimatio tools ca be categorized by t
Aalyzig Software Iflueces o Substrate Noise: A ADC Perspective ByugTae Kag, N. Vijaykrisha, Mary Jae Irwi Samsug, Korea, byugtae.kag@samsug.com Dept. of CSE, Pe State Uiversity, Uiv. Park, PA, USA, vijay@cse.psu.edu,
More informationICM7213. One Second/One Minute Timebase Generator. Features. Description. Ordering Information. Pinout. August 1997
August 997 Features Guarateed V Operatio Very Low Curret Cosumptio (Typ).... µa at V All Outputs TTL Compatible O Chip Oscillator Feedback Resistor Oscillator Requires Oly Exteral compoets: Fixed Capacitor,
More informationDepartment of Electrical and Computer Engineering, Cornell University. ECE 3150: Microelectronics. Spring Due on April 26, 2018 at 7:00 PM
Departmet of Electrical ad omputer Egieerig, orell Uiersity EE 350: Microelectroics Sprig 08 Homework 0 Due o April 6, 08 at 7:00 PM Suggested Readigs: a) Lecture otes Importat Notes: ) MAKE SURE THAT
More information11.11 Two-Channel Filter Banks 1/27
. Two-Chael Filter Baks /7 Two-Chael Filter Baks M We wat to look at methods that are ot based o the DFT I geeral we wat to look at Fig..6 rom Porat ad igure out how to choose i & i to get Perect Reco
More informationCOMPRESSION OF TRANSMULTIPLEXED ACOUSTIC SIGNALS
COMPRESSION OF TRANSMULTIPLEXED ACOUSTIC SIGNALS Mariusz Ziółko, Przemysław Sypka ad Bartosz Ziółko Departmet of Electroics, AGH Uiversity of Sciece ad Techology, al. Mickiewicza 3, 3-59 Kraków, Polad,
More informationSensors & Transducers 2015 by IFSA Publishing, S. L.
Sesors & Trasducers 215 by IFSA Publishig, S. L. http://www.sesorsportal.com Uiversal Sesors ad Trasducers Iterface for Mobile Devices: Metrological Characteristics * Sergey Y. YURISH ad Javier CAÑETE
More informationKMXP SERIES Anisotropic Magneto-Resistive (AMR) Linear Position Sensors
SERIES Aisotropic Mageto-Resistive (AMR) Liear Positio Sesors Positio sesors play a icreasigly importat role i may idustrial, robotic ad medical applicatios. Advaced applicatios i harsh eviromets eed sesors
More informationAcquisition of GPS Software Receiver Using Split-Radix FFT
006 IEEE Coferece o Systems, Ma, ad Cyberetics October -, 006, Taipei, Taiwa Acquisitio of GPS Software Receiver Usig Split-Radix FFT W. H. Li, W. L. Mao, H. W. Tsao, F. R. Chag, ad W. H. Huag Abstract
More informationDesign and Construction of a Three-phase Digital Energy Meter
Desig ad Costructio of a Three-phase Digital Eergy Meter D.P.Chadima, V.G.R.G. Jayawardae, E.A.E.H. Hemachadra, I.N.Jayasekera, H.V.L.Hasaraga, D.C. Hapuarachchi (chadima@elect.mrt.ac.lk, geethagaj@gmail.com,era.hem@gmail.com,ishaivaka@gmail.com,lahiru_hasaraga@yahoo.com,diya_elect.uom@gmail.com)
More informationMath 140 Introductory Statistics
6. Probability Distributio from Data Math Itroductory Statistics Professor Silvia Ferádez Chapter 6 Based o the book Statistics i Actio by A. Watkis, R. Scheaffer, ad G. Cobb. We have three ways of specifyig
More informationCP 405/EC 422 MODEL TEST PAPER - 1 PULSE & DIGITAL CIRCUITS. Time: Three Hours Maximum Marks: 100
PULSE & DIGITAL CIRCUITS Time: Three Hours Maximum Marks: 0 Aswer five questios, takig ANY TWO from Group A, ay two from Group B ad all from Group C. All parts of a questio (a, b, etc. ) should be aswered
More informationFunctional Testing. approach. In this paper, we discuss the effect of phase delay on the. The mixed-signal BIST architecture, illustrated in Fig.
163 39th Southeaster Symposium o System Theory Mercer Uiversity Maco, GA, 31207, March 4-6, 2007 MB3.3 Phase Delay Measuremet ad Calibratio i Built- Aalog Fuctioal Testig Jie Qi, Studet Member, EEE, Charles
More informationFingerprint Classification Based on Directional Image Constructed Using Wavelet Transform Domains
7 Figerprit Classificatio Based o Directioal Image Costructed Usig Wavelet Trasform Domais Musa Mohd Mokji, Syed Abd. Rahma Syed Abu Bakar, Zuwairie Ibrahim 3 Departmet of Microelectroic ad Computer Egieerig
More informationWAAS MOPS: Practical Examples
AAS MOPS: Practical Examples Todd alter Staford Uiversity ABSTRACT The AAS MOPS describes the method by which a ide Area Augmetatio System (AAS) trasmits its differetial GPS correctios ad itegrity iformatio
More informationAME50461 SERIES EMI FILTER HYBRID-HIGH RELIABILITY
PD-94595A AME5046 SERIES EMI FILTER HYBRID-HIGH RELIABILITY Descriptio The AME Series of EMI filters have bee desiged to provide full compliace with the iput lie reflected ripple curret requiremet specified
More informationHigh Speed Area Efficient Modulo 2 1
High Speed Area Efficiet Modulo 2 1 1-Soali Sigh (PG Scholar VLSI, RKDF Ist Bhopal M.P) 2- Mr. Maish Trivedi (HOD EC Departmet, RKDF Ist Bhopal M.P) Adder Abstract Modular adder is oe of the key compoets
More informationA New Basic Unit for Cascaded Multilevel Inverters with the Capability of Reducing the Number of Switches
Joural of Power Electroics, ol, o, pp 67-677, July 67 JPE --6 http://dxdoiorg/6/jpe67 I(Prit: 98-9 / I(Olie: 9-78 A ew Basic Uit for Cascaded Multi Iverters with the Capability of Reducig the umber of
More informationTehrani N Journal of Scientific and Engineering Research, 2018, 5(7):1-7
Available olie www.jsaer.com, 2018, 5(7):1-7 Research Article ISSN: 2394-2630 CODEN(USA): JSERBR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
More informationCounting on r-fibonacci Numbers
Claremot Colleges Scholarship @ Claremot All HMC Faculty Publicatios ad Research HMC Faculty Scholarship 5-1-2015 Coutig o r-fiboacci Numbers Arthur Bejami Harvey Mudd College Curtis Heberle Harvey Mudd
More informationx 1 + x x n n = x 1 x 2 + x x n n = x 2 x 3 + x x n n = x 3 x 5 + x x n = x n
Sectio 6 7A Samplig Distributio of the Sample Meas To Create a Samplig Distributio of the Sample Meas take every possible sample of size from the distributio of x values ad the fid the mea of each sample
More informationADSP ADSP ADSP ADSP. Advanced Digital Signal Processing (18-792) Spring Fall Semester, Department of Electrical and Computer Engineering
ADSP ADSP ADSP ADSP Advaced Digital Sigal Processig (8-79) Sprig Fall Semester, 7 Departmet of Electrical ad Computer Egieerig OTES O RADOM PROCESSES I. Itroductio Radom processes are at the heart of most
More informationTotal Harmonics Distortion Reduction Using Adaptive, Weiner, and Kalman Filters
Wester Michiga Uiversity ScholarWorks at WMU Master's Theses Graduate College 6-2016 Total Harmoics Distortio Reductio Usig Adaptive, Weier, ad Kalma Filters Liqaa Alhafadhi Wester Michiga Uiversity, liquaa.alhafadhi@yahoo.com
More information7. Counting Measure. Definitions and Basic Properties
Virtual Laboratories > 0. Foudatios > 1 2 3 4 5 6 7 8 9 7. Coutig Measure Defiitios ad Basic Properties Suppose that S is a fiite set. If A S the the cardiality of A is the umber of elemets i A, ad is
More informationSubband Coding of Speech Signals Using Decimation and Interpolation
3 th Iteratioal Coferece o AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT- 3, May 6 8, 9, E-Mail: asat@mtc.edu.eg Military Techical College, Kobry Elkobbah, Cairo, Egypt Tel : +() 459 43638, Fax: +() 698
More informationLab 2: Common Source Amplifier.
epartet of Electrical ad Coputer Egieerig Fall 1 Lab : Coo Source plifier. 1. OBJECTIVES Study ad characterize Coo Source aplifier: Bias CS ap usig MOSFET curret irror; Measure gai of CS ap with resistive
More informationGeneral Model :Algorithms in the Real World. Applications. Block Codes
Geeral Model 5-853:Algorithms i the Real World Error Correctig Codes I Overview Hammig Codes Liear Codes 5-853 Page message (m) coder codeword (c) oisy chael decoder codeword (c ) message or error Errors
More informationApplication of Image Fusion to Wireless Image Transmission
Applicatio of Image Fusio to Wireless Image Trasmissio Liae C. Ramac ad Pramod K. Varshey EECS Departmet, Syracuse Uiversity 121 Lik Hall, Syracuse, NY 13244 Email: lcramac@mailbox.syr.edu, varshey@cat.syr.edu
More informationRecovering low frequencies for impedance inversion by frequency domain deconvolution
Recoverig low frequecies for impedace iversio by frequecy domai decovolutio Sia. Esmaeili*, CREWES, Uiversity of Calgary, sesmaeil@ucalgary.ca Gary. Frak. Margrave, CREWES, Uiversity of Calgary, margrave@ucalgary.ca
More informationA SELECTIVE POINTER FORWARDING STRATEGY FOR LOCATION TRACKING IN PERSONAL COMMUNICATION SYSTEMS
A SELETIVE POINTE FOWADING STATEGY FO LOATION TAKING IN PESONAL OUNIATION SYSTES Seo G. hag ad hae Y. Lee Departmet of Idustrial Egieerig, KAIST 373-, Kusug-Dog, Taejo, Korea, 305-70 cylee@heuristic.kaist.ac.kr
More informationUnit 5: Estimating with Confidence
Uit 5: Estimatig with Cofidece Sectio 8.2 The Practice of Statistics, 4 th editio For AP* STARNES, YATES, MOORE Uit 5 Estimatig with Cofidece 8.1 8.2 8.3 Cofidece Itervals: The Basics Estimatig a Populatio
More informationChapter 3. GPS Signal Propagation Characteristics and its Modeling
Chapter 3 GPS Sigal Propagatio Characteristics ad its Modelig 3. Itroductio GPS avigatio sigal icludes vital iformatio such as orbital parameters, clock error coefficiets etc. This received sigal is affected
More informationCircular waveguides. Introduction. Table of Contents
Itroductio Circular waveguides Waveguides ca be simply described as metal pipes. Depedig o their cross sectio there are rectagular waveguides (described i separate tutorial) ad circular waveguides, which
More informationCHAPTER 6 IMPLEMENTATION OF DIGITAL FIR FILTER
CHAPTER 6 IMPLEMENTATION OF DIGITAL FIR FILTER 6.1 INTRODUCTION The digital FIR filters are commo compoets i may digital sigal processig (DSP) systems. There are various applicatios like high speed/low
More informationLossless image compression Using Hashing (using collision resolution) Amritpal Singh 1 and Rachna rajpoot 2
Lossless image compressio Usig Hashig (usig collisio resolutio) Amritpal Sigh 1 ad Racha rajpoot 2 1 M.Tech.* CSE Departmet, 2 Departmet of iformatio techology Guru Kashi UiversityTalwadi Sabo, Bathida
More informationELEC 350 Electronics I Fall 2014
ELEC 350 Electroics I Fall 04 Fial Exam Geeral Iformatio Rough breakdow of topic coverage: 0-5% JT fudametals ad regios of operatio 0-40% MOSFET fudametals biasig ad small-sigal modelig 0-5% iodes (p-juctio
More informationEFFECTS OF GROUNDING SYSTEM ON POWER QUALITY
EFFECTS OF GROUNDING SYSTEM ON POWER QUALITY Bhagat Sigh Tomar, Dwarka Prasad, Apeksha Naredra Rajput Research Scholar, Electrical Egg. Departmet, Laxmi Devi Istitute of Egg. & Techology, Alwar,(Rajastha),Idia
More informationThe Use of Harmonic Information in the Optimal Synthesis of Mechanisms
The Use of Harmoic Iformatio i the Optimal Sythesis of Mechaisms A.M.CONNOR, S.S.DOUGLAS & M.J.GILMARTIN SUMMARY This paper reviews several uses of harmoic iformatio i the sythesis of mechaisms ad shows
More informationThe Firing Dispersion of Bullet Test Sample Analysis
Iteratioal Joural of Materials, Mechaics ad Maufacturig, Vol., No., Ma 5 The Firig Dispersio of Bullet Test Sample Aalsis Youliag Xu, Jubi Zhag, Li Ma, ad Yoghai Sha Udisputed, this approach does reduce
More informationdoi: info:doi/ /ifeec
doi: ifo:doi/1.119/ifeec.17.799153 Trasformer Desig Difficulties of Curret Resoat Coverter for High Power Desity ad Wide Iput ltage Rage Toshiyuki Zaitsu Embedded System Research Ceter Omro Corporatio
More informationCALCULATION OF POWER LOSSES IN UNBALANCED AND HARMONIC POLLUTED ELECTRIC NETWORKS
Aals of the Uiversity of Craiova, Electrical Egieerig series, o. 33, 9; SS 184-485 7 TH TERATOAL COFERECE O ELECTROMECHACAL AD POWER SYSTEMS October 8-9, 9 - aşi, Romaia CALCULATO OF POWER LOSSES UBALACED
More information信號與系統 Signals and Systems
Sprig 2 信號與系統 Sigals ad Systems Chapter SS- Sigals ad Systems Feg-Li Lia NTU-EE Feb Ju Figures ad images used i these lecture otes are adopted from Sigals & Systems by Ala V. Oppeheim ad Ala S. Willsky,
More informationTMCM BLDC MODULE. Reference and Programming Manual
TMCM BLDC MODULE Referece ad Programmig Maual (modules: TMCM-160, TMCM-163) Versio 1.09 August 10 th, 2007 Triamic Motio Cotrol GmbH & Co. KG Sterstraße 67 D 20357 Hamburg, Germay http:www.triamic.com
More information