DIGITAL MEASUREMENT OF POWER SYSTEM HARMONIC MAGNITUDE AND PHASE ANGLE
|
|
- Jasmin Patterson
- 5 years ago
- Views:
Transcription
1 DIGIL MESUREMEN OF POWER SYSEM HRMONIC MGNIUDE ND PHSE NGLE R Micheletti (, R Pieri ( ( Departmet of Electrical Systems ad utomatio, Uiversity of Pisa, Via Diotisalvi, I-566 Pisa, Italy Phoe , Fax , RobertoMicheletti@dseauipiit ( Departmet of Electrical Systems ad utomatio, Uiversity of Pisa, Via Diotisalvi, I-566 Pisa, Italy Phoe , Fax , bstract - he paper deals with the measuremet of harmoic magitude ad phase agle of a periodic voltage v(t i power systems he proposed procedure is based o Walsh spectrum measuremet followed by digital computatio to provide the Fourier spectrum of v(t i magitude ad phase Computer simulatio results are preseted to validate this method Keywords - Harmoic magitude ad phase agle, Power systems, Walsh spectrum, Fourier spectrum INRODUCION he usual represetatio of a periodic time-varyig sigal is the Fourier series he coefficiets of the equatio ca be obtaied accordig to two mai approaches I the first, the iput sigal is sampled, coverted ito digital form ad the Fourier itegral calculatio is used i order to obtai the coefficiets If the period is kow, this method requires oly oe cycle of the sigal: however the mai drawback is the awkward ad the time-cosumig multiplicatios by cosie ad sie coefficiets of Fourier processig Variatios have bee suggested processig the digitized data usig Fast Fourier rasform algorithms: they allow accurate measuremets but the disadvatage is the large amout of computatio ivolved [] I this paper a digital techique of measurig the phase agle of the harmoics as well their magitudes is preseted he method is firstly based o Walsh spectrum measuremet with successive digital computatio to provide the Fourier spectrum of the periodic voltage i magitude ad phase [] his measuremet method is fast ad accurate ad does t require expesive istrumetatio; moreover it is particularly well-suited to power-frequecy waveform measuremets [3]-[6] he Walsh method, i commo with Fourier method, requires that the periodic voltage v(t be frequecy limited, which implies that its Walsh spectrum is made up of a ifiite series of cal ad sal terms However, if the highest harmoic order of v(t is H, the measuremet of oly S cal compoets ad S sal compoets (with S H permits to obtai exactly the Fourier spectrum of v(t except for the roudoff ad trucatio errors i digital processig he extractio of the cosie ad sie coefficiets of v(t from the trucated measure of cal ad sal coefficiets is achieved by way of a Walsh to Fourier matrix coversio process; a subsequet matrix multiplicatio provides for compesatio for the Walsh spectral trucatio he compesatio matrix takes the form of a diagoal matrix with fixed elemets; each coverted Fourier spectral compoet requires to be multiplied by a correctio factor which is fixed for a give harmoic he Walsh method is attractive for use at power system frequecy, for the the sychroizatio of the Walsh waves with v(t is ot difficult It is evidet that Walsh spectra are superior to the Fourier spectra, i that the multiplicatio with sie ad cosie fuctios, respectively, is obviated by simple reversal of sigs (Walsh waves assume values of plus ad mius oe Moreover both odd ad eve harmoics ca be measured PRINCIPLE OF OPERION he Fourier series of a periodic waveform v(t is writte [ a cos t + b si t] v(t a + ω ω ( a b v(t v(t cos si ω t dt ω t ad π/ω is the period of the fudametal frequecy at 5 Hz Walsh fuctios, which are show i Fig up to sal 8 (t, ca be used as a alterative orthogoal family for the series represetatio of a periodic waveform accordig to dt ( (3
2 [ cal (t + sal (t] v(t + (4 v(t cal (t dt (5 v(t sal (t dt (6 v(t wal (t dt (7 S represet the cal spectrum ad sal spectrum of v(t, respectively he elemet of the Walsh to Fourier coversio matrices F a ad F b, are the Fourier coefficiets of the Walsh fuctios cal m (t ad sal m (t, respectively hus S (9 wal(t sal(t cal(t sal(t a, m cal m (t cos ω t dt ( - cal(t - cal4(t - cal6(t - - sal3(t - sal5(t - sal7(t - - cal3(t - cal5(t - cal7(t - - sal4(t - sal6(t - sal8(t - b, m sal m (t si ω t dt ( is the idex of row (correspodig to the harmoic order ad m is the idex of colum Moreover the elemets of the coversio matrix F a assume the same absolute value of the coversio matrix F b, but their sigs may differ he coversio matrices are essetially semiifiite; whe applied i (8 however they are trucated to SxS elemet square matrices lso a additioal matrix multiplicatio is required which compesated for the Walsh spectral trucatio K a a* a K b b* b ( Fig Walsh fuctios up to the eighth order he procedure for the Walsh series determiatio ad the correspodig Fourier derivatio is give below Cosider a periodic voltage v(t whose period is at the fudametal frequecy of 5 Hz Sigal v(t is sampled systematically with samplig frequecy f s he Walsh coefficiets ad are obtaied accordig to (5, (6, (7 o yield the Fourier spectrum of v(t, ad are first multiplied by Walsh-Fourier coversio matrices F a ad F b, respectively, to give approximatios a*, b* to the cosie ad sie coefficiets of v(t: a* F a b* F b (8 a ad b are the desired cosie ad sie coefficiets, respectively he simplest form of compesatio occurs whe S k -, ie, the highest harmoic order i v(t does't exceed the third, or the seveth, or the fifteeth, he compesatio takes the form of a diagoal matrix, with fixed elemets π / si( π / k + k + is the harmoic order 3 COMPUER SIMULION RESULS (3 he measuremet algorithm has bee verified by computer simulatio to ivestigate the validity of this
3 techique he program geerates a iput voltage that is sampled with samplig frequecy f s khz; its waveform is show i Fig ge lta pu tvo I a * time (s Fig Waveform of the iput voltage Let the highest harmoic i the iput voltage be the seveth (ie, k3 ad that the Walsh trucated spectrum, accordig to (4, (5, (6, (7 results wal (t+3546cal (t 6343cal (t+546cal 3 (t- 56cal 4 (t-38cal 5 (t-578cal 6 (t+365cal 7 (t +9593sal (t+964sal (t-463sal 3 (t+3959sal 4 (t -77sal 5 (t-5sal 6 (t-548sal 7 (t I applyig (8 the Fourier spectrum is obtaied i terms of Walsh spectrum b * Next we apply the compesatio matrices (:
4 a v (t time (s Fig 3 Waveform of v(t he results obtaied of magitude ad phase agle of the harmoics are illustrated i able I able I - Magitude ad phase agle of the harmoics b Harmoic order Magitude Phase agle (rad Fig 4 shows the istataeous error of v(t with respect to the iput voltage s we ca see, the istataeous error is withi 5 V hus 5 v(t cos ωt cos ωt 344 cos 3ωt 787 cos 4ωt cos 5ωt cos 6ωt 958 cos 7ωt si ωt si ωt si 3ωt si 4ωt si 5ωt si 6ωt si 7ωt E ror time (s Fig 4 Istataeous error of v(t with respect to the iput voltage Fig 3 shows the waveform of v(t
5 Results obtaied with the proposed method are the compared with those obtaied via the fast Fourier trasform (FF algorithm Fig 5 shows the frequecy cotet of the iput voltage y si t e d l pe ctra s w e r P o Frequecy cotet of the iput voltage Frequecy (Hz Fig 5 Frequecy cotet of the iput voltage Ispectio of Fig 5 cofirms that the proposed method based o Walsh spectrum gives good results compared with those obtaied via the FF algorithm 4 CONCLUSION his paper has described a digital techique of measurig the magitude ad phase agle of the harmoics of a periodic voltage v(t i power systems he method is based o Walsh spectrum measuremet followed by digital computatio for obtaiig the Fourier spectrum his measuremet method is fast ad accurate ad does t require expesive istrumetatio; moreover it is particularly well-suited to power-frequecy waveform measuremets, for the the sychroizatio of the Walsh waves with the iput voltage is ot difficult It is evidet that Walsh spectra are superior to the Fourier spectra, i that the multiplicatio with sie ad cosie fuctios, respectively, is obviated by simple reversal of sigs (Walsh waves assume values ± Moreover both odd ad eve harmoics ca be measured REFERENCES [] Hadbook of Measuremet Sciece Ed by P H Sydeham, New York, Joh Wiley, 98 [] R, Kitai: O-lie measuremet of power system harmoic magitude ad phase agle, IEEE ras Itrum Meas, Vol IM-7,, pp 79-8, 978 [3] DJ, Kish, GH, Heydt: itroductio to power systems aalysis usig Walsh fuctios, Proc North merica Power Symposium IEEE Comp Soc Press, Los lamitos, C, US, pp 48-9, 993 [4] J, Su, H, Grotstolle: Walsh fuctios method for the cotrol of active power filters, Proc Symposium Power Electroics Circuits Hog Kog Polytech, Hog Kog, pp -5, 994 [5] FHJ, ltuve, VI, Diaz, ME, Vazquez: Fourier ad Walsh digital filterig algorithms for distace protectio, Proc IEEE Power Idustry Computer pplicatio Coferece, New York, NY, US, pp 43-8, 995 [6] DV, Coury, HGF, rito: Digital filters applied to computer relayig (of power lies, Proc IEEE Iteratioal Coferece o Power System echology POWERCOM 98, New York, NY, US, pp 6-66, 998
Frequency Response of FIR Filters
EEL335: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we itroduce the idea of the frequecy respose of LTI systems, ad focus specifically o the frequecy respose of FIR filters.. Steady-state
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 informationSignal Processing in Mechatronics. Lecture 3, Convolution, Fourier Series and Fourier Transform
Sigal Processig i Mechatroics Summer semester, 1 Lecture 3, Covolutio, Fourier Series ad Fourier rasform Dr. Zhu K.P. AIS, UM 1 1. Covolutio Covolutio Descriptio of LI Systems he mai premise is that the
More informationSignal Processing in Mechatronics
Sigal Processig i Mechatroics Zhu K.P. AIS, UM. Lecture, Brief itroductio to Sigals ad Systems, Review of Liear Algebra ad Sigal Processig Related Mathematics . Brief Itroductio to Sigals What is sigal
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 informationComplex Algorithms for Lattice Adaptive IIR Notch Filter
4th Iteratioal Coferece o Sigal Processig Systems (ICSPS ) IPCSIT vol. 58 () () IACSIT Press, Sigapore DOI:.7763/IPCSIT..V58. Complex Algorithms for Lattice Adaptive IIR Notch Filter Hog Liag +, Nig Jia
More informationFIR Filter Design: Part II
EEL335: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we cosider how we might go about desigig FIR filters with arbitrary frequecy resposes, through compositio of multiple sigle-peak
More informationOBJECTIVES. Chapter 1 INTRODUCTION TO INSTRUMENTATION FUNCTION AND ADVANTAGES INTRODUCTION. At the end of this chapter, students should be able to:
OBJECTIVES Chapter 1 INTRODUCTION TO INSTRUMENTATION At the ed of this chapter, studets should be able to: 1. Explai the static ad dyamic characteristics of a istrumet. 2. Calculate ad aalyze the measuremet
More informationOrthogonal Gaussian Filters for Signal Processing
Orthogoal Gaussia Filters for Sigal Processig Mark Mackezie ad Kiet Tieu Mechaical Egieerig Uiversity of Wollogog.S.W. Australia Abstract A Gaussia filter usig the Hermite orthoormal series of fuctios
More informationLecture 11: A Fourier Transform Primer
PHYS 34 Fall 1 ecture 11: A Fourier Trasform Primer Ro Reifeberger Birck aotechology Ceter Purdue Uiversity ecture 11 1 f() I may edeavors, we ecouter sigals that eriodically reeat f(t) T t Such reeatig
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 information577. Estimation of surface roughness using high frequency vibrations
577. Estimatio of surface roughess usig high frequecy vibratios V. Augutis, M. Sauoris, Kauas Uiversity of Techology Electroics ad Measuremets Systems Departmet Studetu str. 5-443, LT-5368 Kauas, Lithuaia
More informationExponential Moving Average Pieter P
Expoetial Movig Average Pieter P Differece equatio The Differece equatio of a expoetial movig average lter is very simple: y[] x[] + (1 )y[ 1] I this equatio, y[] is the curret output, y[ 1] is the previous
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science. BACKGROUND EXAM September 30, 2004.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departmet of Electrical Egieerig ad Computer Sciece 6.34 Discrete Time Sigal Processig Fall 24 BACKGROUND EXAM September 3, 24. Full Name: Note: This exam is closed
More informationFilter banks. Separately, the lowpass and highpass filters are not invertible. removes the highest frequency 1/ 2and
Filter bas Separately, the lowpass ad highpass filters are ot ivertible T removes the highest frequecy / ad removes the lowest frequecy Together these filters separate the sigal ito low-frequecy ad high-frequecy
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 informationComparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series
Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series
More informationAnalog and Digital Signals. Introduction to Digital Signal Processing. Discrete-time Sinusoids. Analog and Digital Signals
Itroductio to Digital Sigal Processig Chapter : Itroductio Aalog ad Digital Sigals aalog = cotiuous-time cotiuous amplitude digital = discrete-time discrete amplitude cotiuous amplitude discrete amplitude
More informationChapter 10 Advanced Topics in Random Processes
ery Stark ad Joh W. Woods, Probability, Statistics, ad Radom Variables for Egieers, 4th ed., Pearso Educatio Ic.,. ISBN 978--3-33-6 Chapter Advaced opics i Radom Processes Sectios. Mea-Square (m.s.) Calculus
More information6.003 Homework #12 Solutions
6.003 Homework # Solutios Problems. Which are rue? For each of the D sigals x [] through x 4 [] below), determie whether the coditios listed i the followig table are satisfied, ad aswer for true or F for
More informationDiscrete Orthogonal Moment Features Using Chebyshev Polynomials
Discrete Orthogoal Momet Features Usig Chebyshev Polyomials R. Mukuda, 1 S.H.Og ad P.A. Lee 3 1 Faculty of Iformatio Sciece ad Techology, Multimedia Uiversity 75450 Malacca, Malaysia. Istitute of Mathematical
More informationDiscrete-Time Systems, LTI Systems, and Discrete-Time Convolution
EEL5: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we begi our mathematical treatmet of discrete-time s. As show i Figure, a discrete-time operates or trasforms some iput sequece x [
More informationButterworth LC Filter Designer
Butterworth LC Filter Desiger R S = g g 4 g - V S g g 3 g R L = Fig. : LC filter used for odd-order aalysis g R S = g 4 g V S g g 3 g - R L = useful fuctios ad idetities Uits Costats Table of Cotets I.
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 informationEE260: Digital Design, Spring n Binary Addition. n Complement forms. n Subtraction. n Multiplication. n Inputs: A 0, B 0. n Boolean equations:
EE260: Digital Desig, Sprig 2018 EE 260: Itroductio to Digital Desig Arithmetic Biary Additio Complemet forms Subtractio Multiplicatio Overview Yao Zheg Departmet of Electrical Egieerig Uiversity of Hawaiʻi
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 informationChapter 2 Feedback Control Theory Continued
Chapter Feedback Cotrol Theor Cotiued. Itroductio I the previous chapter, the respose characteristic of simple first ad secod order trasfer fuctios were studied. It was show that first order trasfer fuctio,
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 informationSignals, Instruments, and Systems W4 An Introduction to Signal Processing
Sigals, Istrumets, ad Systems W4 A Itroductio to Sigal Processig Logitude Height y [Pixel] [m] [m] Sigal Amplitude Temperature [ C] Sigal Deiitio A sigal is ay time-varyig or spatial-varyig quatity 0 8
More information6.003 Homework #12 Solutions
6.003 Homework # Solutios Problems. Which are rue? For each of the D sigals x [] through x 4 [] (below), determie whether the coditios listed i the followig table are satisfied, ad aswer for true or F
More information1.3 Convergence Theorems of Fourier Series. k k k k. N N k 1. With this in mind, we state (without proof) the convergence of Fourier series.
.3 Covergece Theorems of Fourier Series I this sectio, we preset the covergece of Fourier series. A ifiite sum is, by defiitio, a limit of partial sums, that is, a cos( kx) b si( kx) lim a cos( kx) b si(
More informationPractical Spectral Anaysis (continue) (from Boaz Porat s book) Frequency Measurement
Practical Spectral Aaysis (cotiue) (from Boaz Porat s book) Frequecy Measuremet Oe of the most importat applicatios of the DFT is the measuremet of frequecies of periodic sigals (eg., siusoidal sigals),
More informationSIGNAL PROCESSING & SIMULATION NEWSLETTER
SIGNAL PROCESSING & SIMULAION NEWSLEER Fourier aalysis made Easy Part Jea Baptiste Joseph, Baro de Fourier, 768-83 While studyig heat coductio i materials, Baro Fourier (a title give to him by Napoleo)
More informationEE 505. Lecture 29. ADC Design. Oversampled
EE 505 Lecture 29 ADC Desig Oversampled Review from Last Lecture SAR ADC V IN Sample Hold C LK V REF DAC DAC Cotroller DAC Cotroller stores estimates of iput i Successive Approximatio Register (SAR) At
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 informationSensitivity Analysis of Daubechies 4 Wavelet Coefficients for Reduction of Reconstructed Image Error
Proceedigs of the 6th WSEAS Iteratioal Coferece o SIGNAL PROCESSING, Dallas, Texas, USA, March -4, 7 67 Sesitivity Aalysis of Daubechies 4 Wavelet Coefficiets for Reductio of Recostructed Image Error DEVINDER
More informationThe z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j
The -Trasform 7. Itroductio Geeralie the complex siusoidal represetatio offered by DTFT to a represetatio of complex expoetial sigals. Obtai more geeral characteristics for discrete-time LTI systems. 7.
More informationAn Improved Proportionate Normalized Least Mean Square Algorithm with Orthogonal Correction Factors for Echo Cancellation
202 Iteratioal Coferece o Electroics Egieerig ad Iformatics (ICEEI 202) IPCSI vol. 49 (202) (202) IACSI Press, Sigapore DOI: 0.7763/IPCSI.202.V49.33 A Improved Proportioate Normalized Least Mea Square
More informationOlli Simula T / Chapter 1 3. Olli Simula T / Chapter 1 5
Sigals ad Systems Sigals ad Systems Sigals are variables that carry iformatio Systemstake sigals as iputs ad produce sigals as outputs The course deals with the passage of sigals through systems T-6.4
More informationEE / EEE SAMPLE STUDY MATERIAL. GATE, IES & PSUs Signal System. Electrical Engineering. Postal Correspondence Course
Sigal-EE Postal Correspodece Course 1 SAMPLE STUDY MATERIAL Electrical Egieerig EE / EEE Postal Correspodece Course GATE, IES & PSUs Sigal System Sigal-EE Postal Correspodece Course CONTENTS 1. SIGNAL
More informationLecture 8: Solving the Heat, Laplace and Wave equations using finite difference methods
Itroductory lecture otes o Partial Differetial Equatios - c Athoy Peirce. Not to be copied, used, or revised without explicit writte permissio from the copyright ower. 1 Lecture 8: Solvig the Heat, Laplace
More informationChapter 4. Fourier Series
Chapter 4. Fourier Series At this poit we are ready to ow cosider the caoical equatios. Cosider, for eample the heat equatio u t = u, < (4.) subject to u(, ) = si, u(, t) = u(, t) =. (4.) Here,
More informationTHE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS
R775 Philips Res. Repts 26,414-423, 1971' THE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS by H. W. HANNEMAN Abstract Usig the law of propagatio of errors, approximated
More informationTHE TRANSFORMATION MATRIX OF CHEBYSHEV IV BERNSTEIN POLYNOMIAL BASES
Joural of Mathematical Aalysis ISSN: 17-341, URL: http://iliriascom/ma Volume 7 Issue 4(16, Pages 13-19 THE TRANSFORMATION MATRIX OF CHEBYSHEV IV BERNSTEIN POLYNOMIAL BASES ABEDALLAH RABABAH, AYMAN AL
More informationResearch Article A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
Discrete Dyamics i Nature ad Society Article ID 210761 4 pages http://dxdoiorg/101155/2014/210761 Research Article A Uified Weight Formula for Calculatig the Sample Variace from Weighted Successive Differeces
More informationModule 18 Discrete Time Signals and Z-Transforms Objective: Introduction : Description: Discrete Time Signal representation
Module 8 Discrete Time Sigals ad Z-Trasforms Objective:To uderstad represetig discrete time sigals, apply z trasform for aalyzigdiscrete time sigals ad to uderstad the relatio to Fourier trasform Itroductio
More informationPolynomial Multiplication and Fast Fourier Transform
Polyomial Multiplicatio ad Fast Fourier Trasform Com S 477/577 Notes Ya-Bi Jia Sep 19, 2017 I this lecture we will describe the famous algorithm of fast Fourier trasform FFT, which has revolutioized digital
More informationChapter 15: Fourier Series
Chapter 5: Fourier Series Ex. 5.3- Ex. 5.3- Ex. 5.- f(t) K is a Fourier Series. he coefficiets are a K; a b for. f(t) AcosZ t is a Fourier Series. a A ad all other coefficiets are zero. Set origi at t,
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 informationVibratory Motion. Prof. Zheng-yi Feng NCHU SWC. National CHung Hsing University, Department of Soil and Water Conservation
Vibratory Motio Prof. Zheg-yi Feg NCHU SWC 1 Types of vibratory motio Periodic motio Noperiodic motio See Fig. A1, p.58 Harmoic motio Periodic motio Trasiet motio impact Trasiet motio earthquake A powerful
More informationSpring 2014, EE123 Digital Signal Processing
Aoucemets EE3 Digital Sigal Processig Last time: FF oday: Frequecy aalysis with DF Widowig Effect of zero-paddig Lecture 9 based o slides by J.M. Kah Spectral Aalysis with the DF Spectral Aalysis with
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 informationSCALING OF NUMBERS IN RESIDUE ARITHMETIC WITH THE FLEXIBLE SELECTION OF SCALING FACTOR
POZNAN UNIVE RSITY OF TE CHNOLOGY ACADE MIC JOURNALS No 76 Electrical Egieerig 203 Zeo ULMAN* Macie CZYŻAK* Robert SMYK* SCALING OF NUMBERS IN RESIDUE ARITHMETIC WITH THE FLEXIBLE SELECTION OF SCALING
More informationFall 2011, EE123 Digital Signal Processing
Lecture 5 Miki Lustig, UCB September 14, 211 Miki Lustig, UCB Motivatios for Discrete Fourier Trasform Sampled represetatio i time ad frequecy umerical Fourier aalysis requires a Fourier represetatio that
More informationThe Discrete Fourier Transform
The iscrete Fourier Trasform The discrete-time Fourier trasform (TFT) of a sequece is a cotiuous fuctio of!, ad repeats with period. I practice we usually wat to obtai the Fourier compoets usig digital
More informationSpectral Analysis. This week in lab. Next classes: 3/26 and 3/28. Your next experiment Homework is to prepare
Spectral Aalysis This week i lab Your ext experimet Homework is to prepare Next classes: 3/26 ad 3/28 Aero Testig, Fracture Toughess Testig Read the Experimets 5 ad 7 sectios of the course maual Spectral
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 informationTMA4205 Numerical Linear Algebra. The Poisson problem in R 2 : diagonalization methods
TMA4205 Numerical Liear Algebra The Poisso problem i R 2 : diagoalizatio methods September 3, 2007 c Eiar M Røquist Departmet of Mathematical Scieces NTNU, N-749 Trodheim, Norway All rights reserved A
More information1. Nature of Impulse Response - Pole on Real Axis. z y(n) = r n. z r
. Nature of Impulse Respose - Pole o Real Axis Causal system trasfer fuctio: Hz) = z yz) = z r z z r y) = r r > : the respose grows mootoically > r > : y decays to zero mootoically r > : oscillatory, decayig
More informationCh3 Discrete Time Fourier Transform
Ch3 Discrete Time Fourier Trasform 3. Show that the DTFT of [] is give by ( k). e k 3. Determie the DTFT of the two sided sigal y [ ],. 3.3 Determie the DTFT of the causal sequece x[ ] A cos( 0 ) [ ],
More informationy[ n] = sin(2" # 3 # n) 50
Period of a Discrete Siusoid y[ ] si( ) 5 T5 samples y[ ] y[ + 5] si() si() [ ] si( 3 ) 5 y[ ] y[ + T] T?? samples [iteger] 5/3 iteger y irratioal frequecy ysi(pisqrt()/5) - - TextEd si( t) T sec cotiuous
More informationExam. Notes: A single A4 sheet of paper (double sided; hand-written or computer typed)
Exam February 8th, 8 Sigals & Systems (5-575-) Prof. R. D Adrea Exam Exam Duratio: 5 Mi Number of Problems: 5 Number of Poits: 5 Permitted aids: Importat: Notes: A sigle A sheet of paper (double sided;
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 informationApply change-of-basis formula to rewrite x as a linear combination of eigenvectors v j.
Eigevalue-Eigevector Istructor: Nam Su Wag eigemcd Ay vector i real Euclidea space of dimesio ca be uiquely epressed as a liear combiatio of liearly idepedet vectors (ie, basis) g j, j,,, α g α g α g α
More informationChapter 2 Systems and Signals
Chapter 2 Systems ad Sigals 1 Itroductio Discrete-Time Sigals: Sequeces Discrete-Time Systems Properties of Liear Time-Ivariat Systems Liear Costat-Coefficiet Differece Equatios Frequecy-Domai Represetatio
More informationThe Discrete Fourier Transform
The Discrete Fourier Trasform Complex Fourier Series Represetatio Recall that a Fourier series has the form a 0 + a k cos(kt) + k=1 b k si(kt) This represetatio seems a bit awkward, sice it ivolves two
More informationCALCULATION OF FIBONACCI VECTORS
CALCULATION OF FIBONACCI VECTORS Stuart D. Aderso Departmet of Physics, Ithaca College 953 Daby Road, Ithaca NY 14850, USA email: saderso@ithaca.edu ad Dai Novak Departmet of Mathematics, Ithaca College
More informationENGI Series Page 6-01
ENGI 3425 6 Series Page 6-01 6. Series Cotets: 6.01 Sequeces; geeral term, limits, covergece 6.02 Series; summatio otatio, covergece, divergece test 6.03 Stadard Series; telescopig series, geometric series,
More informationSolutions. Number of Problems: 4. None. Use only the prepared sheets for your solutions. Additional paper is available from the supervisors.
Quiz November 4th, 23 Sigals & Systems (5-575-) P. Reist & Prof. R. D Adrea Solutios Exam Duratio: 4 miutes Number of Problems: 4 Permitted aids: Noe. Use oly the prepared sheets for your solutios. Additioal
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 informationIntroduction to Distributed Arithmetic. K. Sridharan, IIT Madras
Itroductio to Distriuted rithmetic. Sridhara, IIT Madras Distriuted rithmetic (D) efficiet techique for calculatio of ier product or multipl ad accumulate (MC) The MC operatio is commo i Digital Sigal
More informationChapter 9: Numerical Differentiation
178 Chapter 9: Numerical Differetiatio Numerical Differetiatio Formulatio of equatios for physical problems ofte ivolve derivatives (rate-of-chage quatities, such as velocity ad acceleratio). Numerical
More informationNumerical Conformal Mapping via a Fredholm Integral Equation using Fourier Method ABSTRACT INTRODUCTION
alaysia Joural of athematical Scieces 3(1): 83-93 (9) umerical Coformal appig via a Fredholm Itegral Equatio usig Fourier ethod 1 Ali Hassa ohamed urid ad Teh Yua Yig 1, Departmet of athematics, Faculty
More informationa b c d e f g h Supplementary Information
Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ;
More informationResearch Article Health Monitoring for a Structure Using Its Nonstationary Vibration
Advaces i Acoustics ad Vibratio Volume 2, Article ID 69652, 5 pages doi:.55/2/69652 Research Article Health Moitorig for a Structure Usig Its Nostatioary Vibratio Yoshimutsu Hirata, Mikio Tohyama, Mitsuo
More informationPhys. 201 Mathematical Physics 1 Dr. Nidal M. Ershaidat Doc. 12
Physics Departmet, Yarmouk Uiversity, Irbid Jorda Phys. Mathematical Physics Dr. Nidal M. Ershaidat Doc. Fourier Series Deiitio A Fourier series is a expasio o a periodic uctio (x) i terms o a iiite sum
More informationMAT1026 Calculus II Basic Convergence Tests for Series
MAT026 Calculus II Basic Covergece Tests for Series Egi MERMUT 202.03.08 Dokuz Eylül Uiversity Faculty of Sciece Departmet of Mathematics İzmir/TURKEY Cotets Mootoe Covergece Theorem 2 2 Series of Real
More informationOFFSET CORRECTION IN A DIGITAL INTEGRATOR FOR ROTATING COIL MEASUREMENTS
XX IMEKO World Cogress Metrology for Gree Growth September 9 4, 0, Busa, Republic of Korea OFFSET CORRECTION IN A DIGITAL INTEGRATOR FOR ROTATING COIL MEASUREMENTS P. Arpaia,, P. Cimmio,, L. De Vito, ad
More informationObjective Mathematics
. If sum of '' terms of a sequece is give by S Tr ( )( ), the 4 5 67 r (d) 4 9 r is equal to : T. Let a, b, c be distict o-zero real umbers such that a, b, c are i harmoic progressio ad a, b, c are i arithmetic
More informationEE260: Digital Design, Spring n MUX Gate n Rudimentary functions n Binary Decoders. n Binary Encoders n Priority Encoders
EE260: Digital Desig, Sprig 2018 EE 260: Itroductio to Digital Desig MUXs, Ecoders, Decoders Yao Zheg Departmet of Electrical Egieerig Uiversity of Hawaiʻi at Māoa Overview of Ecoder ad Decoder MUX Gate
More informationLainiotis filter implementation. via Chandrasekhar type algorithm
Joural of Computatios & Modellig, vol.1, o.1, 2011, 115-130 ISSN: 1792-7625 prit, 1792-8850 olie Iteratioal Scietific Press, 2011 Laiiotis filter implemetatio via Chadrasehar type algorithm Nicholas Assimais
More informationDiscrete-Time Signals and Systems. Discrete-Time Signals and Systems. Signal Symmetry. Elementary Discrete-Time Signals.
Discrete-ime Sigals ad Systems Discrete-ime Sigals ad Systems Dr. Deepa Kudur Uiversity of oroto Referece: Sectios. -.5 of Joh G. Proakis ad Dimitris G. Maolakis, Digital Sigal Processig: Priciples, Algorithms,
More informationFinite-length Discrete Transforms. Chapter 5, Sections
Fiite-legth Discrete Trasforms Chapter 5, Sectios 5.2-50 5.0 Dr. Iyad djafar Outlie The Discrete Fourier Trasform (DFT) Matrix Represetatio of DFT Fiite-legth Sequeces Circular Covolutio DFT Symmetry Properties
More informationLecture 7: Fourier Series and Complex Power Series
Math 1d Istructor: Padraic Bartlett Lecture 7: Fourier Series ad Complex Power Series Week 7 Caltech 013 1 Fourier Series 1.1 Defiitios ad Motivatio Defiitio 1.1. A Fourier series is a series of fuctios
More informationSYNTHESIS OF SIGNAL USING THE EXPONENTIAL FOURIER SERIES
SYNTHESIS OF SIGNAL USING THE EXPONENTIAL FOURIER SERIES Sadro Adriao Fasolo ad Luiao Leoel Medes Abstrat I 748, i Itrodutio i Aalysi Ifiitorum, Leohard Euler (707-783) stated the formula exp( jω = os(
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSEMS Versio ECE II, Kharagpur Lesso 8 rasform Codig & K-L rasforms Versio ECE II, Kharagpur Istructioal Oectives At the ed of this lesso, the studets should e ale to:.
More informationControl Charts for Mean for Non-Normally Correlated Data
Joural of Moder Applied Statistical Methods Volume 16 Issue 1 Article 5 5-1-017 Cotrol Charts for Mea for No-Normally Correlated Data J. R. Sigh Vikram Uiversity, Ujjai, Idia Ab Latif Dar School of Studies
More informationDiscrete-Time Signals and Systems. Signals and Systems. Digital Signals. Discrete-Time Signals. Operations on Sequences: Basic Operations
-6.3 Digital Sigal Processig ad Filterig..8 Discrete-ime Sigals ad Systems ime-domai Represetatios of Discrete-ime Sigals ad Systems ime-domai represetatio of a discrete-time sigal as a sequece of umbers
More informationDesign of distribution transformer loss meter considering the harmonic loss based on one side measurement method
3rd Iteratioal Coferece o Machiery, Materials ad Iformatio Techology Applicatios (ICMMITA 05) Desig of distributio trasformer loss meter cosiderig the harmoic loss based o oe side measuremet method HU
More informationSinusoidal Steady-state Analysis
Siusoidal Steady-state Aalysis Complex umber reviews Phasors ad ordiary differetial equatios Complete respose ad siusoidal steady-state respose Cocepts of impedace ad admittace Siusoidal steady-state aalysis
More informationx x x Using a second Taylor polynomial with remainder, find the best constant C so that for x 0,
Math Activity 9( Due with Fial Eam) Usig first ad secod Taylor polyomials with remaider, show that for, 8 Usig a secod Taylor polyomial with remaider, fid the best costat C so that for, C 9 The th Derivative
More information6.003: Signal Processing
6.003: Sigal Processig Discrete-Time Fourier Series orthogoality of harmoically related DT siusoids DT Fourier series relatios differeces betwee CT ad DT Fourier series properties of DT Fourier series
More informationThe z-transform can be used to obtain compact transform-domain representations of signals and systems. It
3 4 5 6 7 8 9 10 CHAPTER 3 11 THE Z-TRANSFORM 31 INTRODUCTION The z-trasform ca be used to obtai compact trasform-domai represetatios of sigals ad systems It provides ituitio particularly i LTI system
More informationCHM 424 EXAM 2 - COVER PAGE FALL
CHM 44 EXAM - COVER PAGE FALL 007 There are six umbered pages with five questios. Aswer the questios o the exam. Exams doe i ik are eligible for regrade, those doe i pecil will ot be regraded. coulomb
More informationBalancing. Rotating Components Examples of rotating components in a mechanism or a machine. (a)
alacig NOT COMPLETE Rotatig Compoets Examples of rotatig compoets i a mechaism or a machie. Figure 1: Examples of rotatig compoets: camshaft; crakshaft Sigle-Plae (Static) alace Cosider a rotatig shaft
More informationAH Checklist (Unit 3) AH Checklist (Unit 3) Matrices
AH Checklist (Uit 3) AH Checklist (Uit 3) Matrices Skill Achieved? Kow that a matrix is a rectagular array of umbers (aka etries or elemets) i paretheses, each etry beig i a particular row ad colum Kow
More informationStopping oscillations of a simple harmonic oscillator using an impulse force
It. J. Adv. Appl. Math. ad Mech. 5() (207) 6 (ISSN: 2347-2529) IJAAMM Joural homepage: www.ijaamm.com Iteratioal Joural of Advaces i Applied Mathematics ad Mechaics Stoppig oscillatios of a simple harmoic
More informationGenerating Functions for Laguerre Type Polynomials. Group Theoretic method
It. Joural of Math. Aalysis, Vol. 4, 2010, o. 48, 257-266 Geeratig Fuctios for Laguerre Type Polyomials α of Two Variables L ( xy, ) by Usig Group Theoretic method Ajay K. Shula* ad Sriata K. Meher** *Departmet
More informationFour-dimensional Vector Matrix Determinant and Inverse
I.J. Egieerig ad Maufacturig 013 30-37 Published Olie Jue 01 i MECS (http://www.mecs-press.et) DOI: 10.5815/iem.01.03.05 vailable olie at http://www.mecs-press.et/iem Four-dimesioal Vector Matrix Determiat
More informationHARMONIC ANALYSIS FOR OPTICALLY MODULATING BODIES USING THE HARMONIC STRUCTURE FUNCTION (HSF) Lockheed Martin Hawaii
HARMONIC ANALYSIS FOR OPTICALLY MODULATING BODIES USING THE HARMONIC STRUCTURE FUNCTION (HSF) Dr. R. David Dikema Chief Scietist Mr. Scot Seto Chief Egieer Lockheed Marti Hawaii Abstract Lockheed Marti
More information