The Excel FFT Function v1.1 P. T. Debevec February 12, The discrete Fourier transform may be used to identify periodic structures in time ht.
|
|
- Annice Caldwell
- 6 years ago
- Views:
Transcription
1 The Excel FFT Fucti v P T Debevec February 2, 26 The discrete Furier trasfrm may be used t idetify peridic structures i time ht series data Suppse that a physical prcess is represeted by the fucti f time, ( ) The fucti is sampled at times, t = t where =,, 2,, Frm these measuremets, h, cmplex amplitudes, H, are determied which satisfy the equatis H = 2π i = h e The sampled fucti the has the discrete Furier expasi 2π i h = He This equati ca be cast i familiar frm with ( ) ( ) = 2π = 2π T T = ω t = ωt h iω t He = = The right-had side is the discrete aalgue t the cmplex frm f the Furier expasi where the cmplex cefficiets, i t ht () = ce ω =, are give by c iωt c = ht () e dt T T The Excel data aalysis pacage has a Furier aalysis rutie which calculates the cmplex cefficiets, H, frm the time series data, h The rutie requires that the umber f samples i the time series data be a pwer f 2, ie = 2 m The example i this te uses = 248 The Excel fucti is t well dcumeted, but it is straightfrward t use This te describes the Excel wrsheet, Furier_examplexls, which is i the Physics 4 web site uder Tutrials ad Lectures, Experimet
2 The time series data i this example are btaied frm samplig a fucti describig the free decay f a trsi scillatr fr time t > t, () ( ) ( π ( )) at t θ t = Ae si 2 f t t The fucti is calculated i time steps f 2 s, which crrespds t samplig rate f 5 Hz The time series data are shw i the Fig belw free decay damped scillatr raw cuts time (s) Fig Plt f time series data decay f trsi scillatr The data ccupy cells B3 t B25 i the data wrsheet f the wrb Clic Tls i the Excel meu bar, ad select Data Aalysis I Data Aalysis select Furier Aalysis, ad a simple dialg bx appears The dialg bx is shw belw i Fig 2 Fig 2 Furier Aalysis dialg bx
3 Fr Iput Rage eter $B$3:$B$25, the lcati f the time series data, ad fr utput rage eter a cveiet place the wrsheet, fr example, $J$3:$J$25 After selectig the OK butt, Excel returs i clum J the cmplex cefficiets, 248 f them A prti f clum J is shw i Fig 3 belw Fig 3 Prti f Excel wrsheet shwig FFT utput Excel isists i displayig 5 digits fr bth the real ad imagiary part f the cefficiet, ad thus the utput ccupies csider space Examiati f the clum f cmplex umbers shws that the first etry (i cell J3) ad the 25 th etry (i cell J27) are real These cells represet the cefficiets fr the zer frequecy ad the fldig frequecy, f Sice the data were sampled at 5 Hz, the fldig frequecy is ½ 5 Hz = 25 Hz c Cells J3 thrugh J27 represet the cmplex cefficiets fr 2+ frequecies frm Hz t 25 Hz The frequecy icremet is the f = fc It is cveiet t mae a clum f frequecies ext t the clum f cefficiets This clum icludes cells I3 t I27 The Furier Aalysis rutie perates ly the time series data The crrespdece betwee frequecy ad cmplex cefficiet must be calculated idepedetly The 23 etries frm cell J28 t cell J25 are idetical t the 23 etries frm cell J26 t J4 These etries ctai additial ifrmati, ad they culd have bee mitted frm the display The Furier Aalysis f time series data yields the cmplex cefficiets fr ly 2+ frequecies The pwer i each frequecy bi is prprtial t the square f the mdulus f the cmplex cefficiet The cstat f prprtiality adpted i this te has the prperty that the mea squared amplitude f the time series data is equal t the ttal pwer i the frequecy dmai as shw belw Excel has a umber f fuctis fr cmplex argumets Multiplicati f tw cmplex umbers is accmplished with the fucti IMPRODUCT(z, z 2 ) Multiplicati f the cefficiets i clum J by prduces the rmalized cefficiets i clum The abslute value f a cmplex umber is accmplished with the fucti IMABS(z) Applyig the IMABS fucti t the rmalized cefficiets i clum ad multiplyig by a factr f 2 prduces the magitude f the Furier cefficiets i clum P The magitude f the Furier cefficiets as a fucti f frequecy is shw i Fig 4 belw The maximum value ccurs i the frequecy bi at 4883 Hz
4 magitude f Furier amplitude magitude f Furier amplitude versus frequecy frequecy (Hz) Fig 4 Magitude f rmalized Furier cefficiet versus frequecy Fially, the pwer at each frequecy (except zer frequecy) is the square f the magitude The pwer is calculated i clum Q ad shw i Fig 5 belw The pwer at zer frequecy is the square f the magitude divided by 2 This factr f 2 als appears i -discrete Furier aalysis This pwer distributi is characteristic f expetial decay E+5 Furier pwer versus frequecy E+3 Furier pwer E+ E- E frequecy (Hz) Fig 5 Furier pwer versus frequecy
5 The rmalizati adpted i this te has a cveiet prperty Defie the mea squared amplitude f the time series data as θ = mea squred amplitude = ( ) 2 t The square f the amplitude is calculated i clum C The mea squared amplitude is calculated i cell F9 Fr these data it has the value f A pure sie wave with a amplitude f 2, fr which a itegral umber f perids ccur i the ttal sampled time, has a mea squared amplitude f uity Thus the mea squared amplitude has the same rle as the rms value f a peridic fucti The ttal Furier pwer, the sum f the etries i clum Q, is calculated i cell G9 Fr these data it als has the value f , because f the rmalizati If ly the relative pwer i differet frequecy bis is eeded, the the rmalizati is t required The relative pwer is give by the square f the mdulus f the Excel utput directly
D.S.G. POLLOCK: TOPICS IN TIME-SERIES ANALYSIS STATISTICAL FOURIER ANALYSIS
STATISTICAL FOURIER ANALYSIS The Furier Represetati f a Sequece Accrdig t the basic result f Furier aalysis, it is always pssible t apprximate a arbitrary aalytic fucti defied ver a fiite iterval f the
More informationMATH Midterm Examination Victor Matveev October 26, 2016
MATH 33- Midterm Examiati Victr Matveev Octber 6, 6. (5pts, mi) Suppse f(x) equals si x the iterval < x < (=), ad is a eve peridic extesi f this fucti t the rest f the real lie. Fid the csie series fr
More informationFourier Series & Fourier Transforms
Experimet 1 Furier Series & Furier Trasfrms MATLAB Simulati Objectives Furier aalysis plays a imprtat rle i cmmuicati thery. The mai bjectives f this experimet are: 1) T gai a gd uderstadig ad practice
More informationQuantum Mechanics for Scientists and Engineers. David Miller
Quatum Mechaics fr Scietists ad Egieers David Miller Time-depedet perturbati thery Time-depedet perturbati thery Time-depedet perturbati basics Time-depedet perturbati thery Fr time-depedet prblems csider
More information(b) y(t) is not periodic although sin t and 4 cos 2πt are independently periodic.
Chapter 7, Sluti. (a) his is peridic with ω which leads t /ω. (b) y(t) is t peridic althugh si t ad cs t are idepedetly peridic. (c) Sice si A cs B.5[si(A B) si(a B)], g(t) si t cs t.5[si 7t si( t)].5
More informationMATHEMATICS 9740/01 Paper 1 14 Sep hours
Cadidate Name: Class: JC PRELIMINARY EXAM Higher MATHEMATICS 9740/0 Paper 4 Sep 06 3 hurs Additial Materials: Cver page Aswer papers List f Frmulae (MF5) READ THESE INSTRUCTIONS FIRST Write yur full ame
More informationAxial Temperature Distribution in W-Tailored Optical Fibers
Axial Temperature Distributi i W-Tailred Optical ibers Mhamed I. Shehata (m.ismail34@yah.cm), Mustafa H. Aly(drmsaly@gmail.cm) OSA Member, ad M. B. Saleh (Basheer@aast.edu) Arab Academy fr Sciece, Techlgy
More information5.80 Small-Molecule Spectroscopy and Dynamics
MIT OpeCurseWare http://cw.mit.edu 5.8 Small-Mlecule Spectrscpy ad Dyamics Fall 8 Fr ifrmati abut citig these materials r ur Terms f Use, visit: http://cw.mit.edu/terms. 5.8 Lecture #33 Fall, 8 Page f
More informationare specified , are linearly independent Otherwise, they are linearly dependent, and one is expressed by a linear combination of the others
Chater 3. Higher Order Liear ODEs Kreyszig by YHLee;4; 3-3. Hmgeeus Liear ODEs The stadard frm f the th rder liear ODE ( ) ( ) = : hmgeeus if r( ) = y y y y r Hmgeeus Liear ODE: Suersiti Pricile, Geeral
More informationA Hartree-Fock Calculation of the Water Molecule
Chemistry 460 Fall 2017 Dr. Jea M. Stadard Nvember 29, 2017 A Hartree-Fck Calculati f the Water Mlecule Itrducti A example Hartree-Fck calculati f the water mlecule will be preseted. I this case, the water
More informationChapter 3.1: Polynomial Functions
Ntes 3.1: Ply Fucs Chapter 3.1: Plymial Fuctis I Algebra I ad Algebra II, yu ecutered sme very famus plymial fuctis. I this secti, yu will meet may ther members f the plymial family, what sets them apart
More information[1 & α(t & T 1. ' ρ 1
NAME 89.304 - IGNEOUS & METAMORPHIC PETROLOGY DENSITY & VISCOSITY OF MAGMAS I. Desity The desity (mass/vlume) f a magma is a imprtat parameter which plays a rle i a umber f aspects f magma behavir ad evluti.
More informationThe Acoustical Physics of a Standing Wave Tube
UIUC Physics 93POM/Physics 406POM The Physics f Music/Physics f Musical Istrumets The Acustical Physics f a Stadig Wave Tube A typical cylidrical-shaped stadig wave tube (SWT) {aa impedace tube} f legth
More informationExamination No. 3 - Tuesday, Nov. 15
NAME (lease rit) SOLUTIONS ECE 35 - DEVICE ELECTRONICS Fall Semester 005 Examiati N 3 - Tuesday, Nv 5 3 4 5 The time fr examiati is hr 5 mi Studets are allwed t use 3 sheets f tes Please shw yur wrk, artial
More informationPhysical Chemistry Laboratory I CHEM 445 Experiment 2 Partial Molar Volume (Revised, 01/13/03)
Physical Chemistry Labratry I CHEM 445 Experimet Partial Mlar lume (Revised, 0/3/03) lume is, t a gd apprximati, a additive prperty. Certaily this apprximati is used i preparig slutis whse ccetratis are
More informationENGI 4421 Central Limit Theorem Page Central Limit Theorem [Navidi, section 4.11; Devore sections ]
ENGI 441 Cetral Limit Therem Page 11-01 Cetral Limit Therem [Navidi, secti 4.11; Devre sectis 5.3-5.4] If X i is t rmally distributed, but E X i, V X i ad is large (apprximately 30 r mre), the, t a gd
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 informationSolutions. Definitions pertaining to solutions
Slutis Defiitis pertaiig t slutis Slute is the substace that is disslved. It is usually preset i the smaller amut. Slvet is the substace that des the disslvig. It is usually preset i the larger amut. Slubility
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 informationDynamic Response of Second Order Mechanical Systems with Viscous Dissipation forces
Hadut #a (pp. 1-39) Dyamic Respse f Secd Order Mechaical Systems with Viscus Dissipati frces d X d X + + = ext() t M D K X F dt dt Free Respse t iitial cditis ad F (t) = 0, Uderdamped, Critically Damped
More informationA Study on Estimation of Lifetime Distribution with Covariates Under Misspecification
Prceedigs f the Wrld Cgress Egieerig ad Cmputer Sciece 2015 Vl II, Octber 21-23, 2015, Sa Fracisc, USA A Study Estimati f Lifetime Distributi with Cvariates Uder Misspecificati Masahir Ykyama, Member,
More informationComplex Numbers Solutions
Complex Numbers Solutios Joseph Zoller February 7, 06 Solutios. (009 AIME I Problem ) There is a complex umber with imagiary part 64 ad a positive iteger such that Fid. [Solutio: 697] 4i + + 4i. 4i 4i
More informationReview for cumulative test
Hrs Math 3 review prblems Jauary, 01 cumulative: Chapters 1- page 1 Review fr cumulative test O Mday, Jauary 7, Hrs Math 3 will have a curse-wide cumulative test cverig Chapters 1-. Yu ca expect the test
More information, the random variable. and a sample size over the y-values 0:1:10.
Lecture 3 (4//9) 000 HW PROBLEM 3(5pts) The estimatr i (c) f PROBLEM, p 000, where { } ~ iid bimial(,, is 000 e f the mst ppular statistics It is the estimatr f the ppulati prprti I PROBLEM we used simulatis
More informationLecture 21: Signal Subspaces and Sparsity
ECE 830 Fall 00 Statistical Sigal Prcessig istructr: R. Nwak Lecture : Sigal Subspaces ad Sparsity Sigal Subspaces ad Sparsity Recall the classical liear sigal mdel: X = H + w, w N(0, where S = H, is a
More informationChapter 5. Root Locus Techniques
Chapter 5 Rt Lcu Techique Itrducti Sytem perfrmace ad tability dt determied dby cled-lp l ple Typical cled-lp feedback ctrl ytem G Ope-lp TF KG H Zer -, - Ple 0, -, - K Lcati f ple eaily fud Variati f
More informationESWW-2. Israeli semi-underground great plastic scintillation multidirectional muon telescope (ISRAMUTE) for space weather monitoring and forecasting
ESWW-2 Israeli semi-udergrud great plastic scitillati multidirectial mu telescpe (ISRAMUTE) fr space weather mitrig ad frecastig L.I. Drma a,b, L.A. Pustil'ik a, A. Sterlieb a, I.G. Zukerma a (a) Israel
More informationGrade 3 Mathematics Course Syllabus Prince George s County Public Schools
Ctet Grade 3 Mathematics Curse Syllabus Price Gerge s Cuty Public Schls Prerequisites: Ne Curse Descripti: I Grade 3, istructial time shuld fcus fur critical areas: (1) develpig uderstadig f multiplicati
More informationIntermediate Division Solutions
Itermediate Divisi Slutis 1. Cmpute the largest 4-digit umber f the frm ABBA which is exactly divisible by 7. Sluti ABBA 1000A + 100B +10B+A 1001A + 110B 1001 is divisible by 7 (1001 7 143), s 1001A is
More informationAuthor. Introduction. Author. o Asmir Tobudic. ISE 599 Computational Modeling of Expressive Performance
ISE 599 Cmputatial Mdelig f Expressive Perfrmace Playig Mzart by Aalgy: Learig Multi-level Timig ad Dyamics Strategies by Gerhard Widmer ad Asmir Tbudic Preseted by Tsug-Ha (Rbert) Chiag April 5, 2006
More informationLecture 18. MSMPR Crystallization Model
ecture 18. MSMPR Crystalliati Mdel MSMPR Crystalliati Mdel Crystal-Ppulati alace - Number f crystals - Cumulative umber f crystals - Predmiat crystal sie - Grwth rate MSMPR Crystalliati Mdel Mixed-suspesi,
More informationStudy of Energy Eigenvalues of Three Dimensional. Quantum Wires with Variable Cross Section
Adv. Studies Ther. Phys. Vl. 3 009. 5 3-0 Study f Eergy Eigevalues f Three Dimesial Quatum Wires with Variale Crss Secti M.. Sltai Erde Msa Departmet f physics Islamic Aad Uiversity Share-ey rach Ira alrevahidi@yah.cm
More informationCHAPTER 5. Solutions for Exercises
HAPTE 5 Slutins fr Exercises E5. (a We are given v ( t 50 cs(00π t 30. The angular frequency is the cefficient f t s we have ω 00π radian/s. Then f ω / π 00 Hz T / f 0 ms m / 50 / 06. Furthermre, v(t attains
More informationE o and the equilibrium constant, K
lectrchemical measuremets (Ch -5 t 6). T state the relati betwee ad K. (D x -b, -). Frm galvaic cell vltage measuremet (a) K sp (D xercise -8, -) (b) K sp ad γ (D xercise -9) (c) K a (D xercise -G, -6)
More informationSound Absorption Characteristics of Membrane- Based Sound Absorbers
Purdue e-pubs Publicatis f the Ray W. Schl f Mechaical Egieerig 8-28-2003 Sud Absrpti Characteristics f Membrae- Based Sud Absrbers J Stuart Blt, blt@purdue.edu Jih Sg Fllw this ad additial wrks at: http://dcs.lib.purdue.edu/herrick
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 informationDesign and Implementation of Cosine Transforms Employing a CORDIC Processor
C16 1 Desig ad Implemetati f Csie Trasfrms Emplyig a CORDIC Prcessr Sharaf El-Di El-Nahas, Ammar Mttie Al Hsaiy, Magdy M. Saeb Arab Academy fr Sciece ad Techlgy, Schl f Egieerig, Alexadria, EGYPT ABSTRACT
More informationACTIVE FILTERS EXPERIMENT 2 (EXPERIMENTAL)
EXPERIMENT ATIVE FILTERS (EXPERIMENTAL) OBJETIVE T desig secd-rder lw pass ilters usig the Salle & Key (iite psitive- gai) ad iiite-gai apliier dels. Oe circuit will exhibit a Butterwrth respse ad the
More informationANALOG FILTERS. C. Sauriol. Algonquin College Ottawa, Ontario
LOG ILT By. auril lgqui llege Ottawa, Otari ev. March 4, 003 TBL O OTT alg ilters TIO PI ILT. irst-rder lw-pass filter- -4. irst-rder high-pass filter- 4-6 3. ecd-rder lw-pass filter- 6-4. ecd-rder bad-pass
More informationK [f(t)] 2 [ (st) /2 K A GENERALIZED MEIJER TRANSFORMATION. Ku(z) ()x) t -)-I e. K(z) r( + ) () (t 2 I) -1/2 e -zt dt, G. L. N. RAO L.
Iterat. J. Math. & Math. Scl. Vl. 8 N. 2 (1985) 359-365 359 A GENERALIZED MEIJER TRANSFORMATION G. L. N. RAO Departmet f Mathematics Jamshedpur C-perative Cllege f the Rachi Uiversity Jamshedpur, Idia
More informationSection 10.3 The Complex Plane; De Moivre's Theorem. abi
Sectio 03 The Complex Plae; De Moivre's Theorem REVIEW OF COMPLEX NUMBERS FROM COLLEGE ALGEBRA You leared about complex umbers of the form a + bi i your college algebra class You should remember that "i"
More informationIdentical Particles. We would like to move from the quantum theory of hydrogen to that for the rest of the periodic table
We wuld like t ve fr the quatu thery f hydrge t that fr the rest f the peridic table Oe electr at t ultielectr ats This is cplicated by the iteracti f the electrs with each ther ad by the fact that the
More informationBIO752: Advanced Methods in Biostatistics, II TERM 2, 2010 T. A. Louis. BIO 752: MIDTERM EXAMINATION: ANSWERS 30 November 2010
BIO752: Advaced Methds i Bistatistics, II TERM 2, 2010 T. A. Luis BIO 752: MIDTERM EXAMINATION: ANSWERS 30 Nvember 2010 Questi #1 (15 pits): Let X ad Y be radm variables with a jit distributi ad assume
More informationSTRUCTURES IN MIKE 21. Flow over sluice gates A-1
A-1 STRUCTURES IN MIKE 1 Fl ver luice gate Fr a give gemetry f the luice gate ad k ater level uptream ad dtream f the tructure, the fl rate, ca be determied thrugh the equati f eergy ad mmetum - ee B Pedere,
More informationHº = -690 kj/mol for ionization of n-propylene Hº = -757 kj/mol for ionization of isopropylene
Prblem 56. (a) (b) re egative º values are a idicati f mre stable secies. The º is mst egative fr the i-ryl ad -butyl is, bth f which ctai a alkyl substituet bded t the iized carb. Thus it aears that catis
More informationChapter 1: Fundamentals
Chapter 1: Fudametals 1.1 Real Numbers Irratial umbers are real umbers that cat be expressed as ratis f itegers. That such umbers exist was a prfud embarrassmet t the Pythagrea brtherhd, ad they are said
More informationUNIVERSITY OF TECHNOLOGY. Department of Mathematics PROBABILITY THEORY, STATISTICS AND OPERATIONS RESEARCH GROUP. Memorandum COSOR 76-10
EI~~HOVEN UNIVERSITY OF TECHNOLOGY Departmet f Mathematics PROBABILITY THEORY, STATISTICS AND OPERATIONS RESEARCH GROUP Memradum COSOR 76-10 O a class f embedded Markv prcesses ad recurrece by F.H. Sims
More informationWavelet Video with Unequal Error Protection Codes in W-CDMA System and Fading Channels
Wavelet Vide with Uequal Errr Prtecti Cdes i W-CDMA System ad Fadig Chaels MINH HUNG LE ad RANJITH LIYANA-PATHIRANA Schl f Egieerig ad Idustrial Desig Cllege f Sciece, Techlgy ad Evirmet Uiversity f Wester
More informationWEST VIRGINIA UNIVERSITY
WEST VIRGINIA UNIVERSITY PLASMA PHYSICS GROUP INTERNAL REPORT PL - 045 Mea Optical epth ad Optical Escape Factr fr Helium Trasitis i Helic Plasmas R.F. Bivi Nvember 000 Revised March 00 TABLE OF CONTENT.0
More informationMechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter
Time Respose & Frequecy Respose d -Order Dyamic System -Pole, Low-Pass, Active Filter R 4 R 7 C 5 e i R 1 C R 3 - + R 6 - + e out Assigmet: Perform a Complete Dyamic System Ivestigatio of the Two-Pole,
More informationCoupled Inductors and Transformers
Cupled nductrs and Transfrmers Self-nductance When current i flws thrugh the cil, a magnetic flux is prduced arund it. d d di di v= = = dt di dt dt nductance: = d di This inductance is cmmnly called self-inductance,
More informationFrequency-Domain Study of Lock Range of Injection-Locked Non- Harmonic Oscillators
0 teratial Cferece mage Visi ad Cmputig CVC 0 PCST vl. 50 0 0 ACST Press Sigapre DO: 0.776/PCST.0.V50.6 Frequecy-Dmai Study f Lck Rage f jecti-lcked N- armic Oscillatrs Yushi Zhu ad Fei Yua Departmet f
More informationx 2 x 3 x b 0, then a, b, c log x 1 log z log x log y 1 logb log a dy 4. dx As tangent is perpendicular to the x axis, slope
The agle betwee the tagets draw t the parabla y = frm the pit (-,) 5 9 6 Here give pit lies the directri, hece the agle betwee the tagets frm that pit right agle Ratig :EASY The umber f values f c such
More informationGeneral Chemistry 1 (CHEM1141) Shawnee State University Fall 2016
Geeral Chemistry 1 (CHEM1141) Shawee State Uiversity Fall 2016 September 23, 2016 Name E x a m # I C Please write yur full ame, ad the exam versi (IC) that yu have the scatr sheet! Please 0 check the bx
More informationALE 26. Equilibria for Cell Reactions. What happens to the cell potential as the reaction proceeds over time?
Name Chem 163 Secti: Team Number: AL 26. quilibria fr Cell Reactis (Referece: 21.4 Silberberg 5 th editi) What happes t the ptetial as the reacti prceeds ver time? The Mdel: Basis fr the Nerst quati Previusly,
More informationLecture 7: Damped and Driven Oscillations
Lecture 7: Damped and Driven Oscillatins Last time, we fund fr underdamped scillatrs: βt x t = e A1 + A csω1t + i A1 A sinω1t A 1 and A are cmplex numbers, but ur answer must be real Implies that A 1 and
More informationRates and Mechanisms of Chemical Reactions
Rates ad Mechaisms f Chemical Reactis Why sme rxs prceed very fast ad thers require days, mths r eve years t prduce a detectable amt f prduct? H (g) + F (g) HF (g) (very fast) 3 H (g) + N (g) NH 3 (g)
More informationControl Systems. Controllability and Observability (Chapter 6)
6.53 trl Systems trllaility ad Oservaility (hapter 6) Geeral Framewrk i State-Spae pprah Give a LTI system: x x u; y x (*) The system might e ustale r des t meet the required perfrmae spe. Hw a we imprve
More informationECEN 4872/5827 Lecture Notes
ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals
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 information5.1 Two-Step Conditional Density Estimator
5.1 Tw-Step Cditial Desity Estimatr We ca write y = g(x) + e where g(x) is the cditial mea fucti ad e is the regressi errr. Let f e (e j x) be the cditial desity f e give X = x: The the cditial desity
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 informationLecture 3: Divide and Conquer: Fast Fourier Transform
Lecture 3: Divide ad Coquer: Fast Fourier Trasform Polyomial Operatios vs. Represetatios Divide ad Coquer Algorithm Collapsig Samples / Roots of Uity FFT, IFFT, ad Polyomial Multiplicatio Polyomial operatios
More informationEvery gas consists of a large number of small particles called molecules moving with very high velocities in all possible directions.
Kietic thery f gases ( Kietic thery was develped by Berlli, Jle, Clasis, axwell ad Bltzma etc. ad represets dyamic particle r micrscpic mdel fr differet gases sice it thrws light the behir f the particles
More informationENGI 4421 Central Limit Theorem Page Central Limit Theorem [Navidi, section 4.11; Devore sections ]
ENGI 441 Cetral Limit Therem Page 11-01 Cetral Limit Therem [Navidi, secti 4.11; Devre sectis 5.3-5.4] If X i is t rmally distributed, but E X i, V X i ad is large (apprximately 30 r mre), the, t a gd
More informationProblem 1. Problem Engineering Dynamics Problem Set 9--Solution. Find the equation of motion for the system shown with respect to:
2.003 Egieerig Dyamics Problem Set 9--Solutio Problem 1 Fid the equatio of motio for the system show with respect to: a) Zero sprig force positio. Draw the appropriate free body diagram. b) Static equilibrium
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 information1the 1it is said to be overdamped. When 1, the roots of
Homework 3 AERE573 Fall 08 Due 0/8(M) ame PROBLEM (40pts) Cosider a D order uderdamped system trasfer fuctio H( s) s ratio 0 The deomiator is the system characteristic polyomial P( s) s s (a)(5pts) Use
More informationComparative analysis of bayesian control chart estimation and conventional multivariate control chart
America Jural f Theretical ad Applied Statistics 3; ( : 7- ublished lie Jauary, 3 (http://www.sciecepublishiggrup.cm//atas di:.648/.atas.3. Cmparative aalysis f bayesia ctrl chart estimati ad cvetial multivariate
More informationElectrostatics. . where,.(1.1) Maxwell Eqn. Total Charge. Two point charges r 12 distance apart in space
Maxwell Eq. E ρ Electrstatics e. where,.(.) first term is the permittivity i vacuum 8.854x0 C /Nm secd term is electrical field stregth, frce/charge, v/m r N/C third term is the charge desity, C/m 3 E
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 informationOn the structure of space-time and matter as obtained from the Planck scale by period doubling in three and four dimensions
O the structure f space-time ad matter as btaied frm the Plack scale by perid dublig i three ad fur dimesis Ari Leht Helsiki Uiversity f Techlgy Labratry f Materials Sciece P.O. Bx 600, FIN-0150 HUT Oe
More informationThe Random Walk For Dummies
The Radom Walk For Dummies Richard A Mote Abstract We look at the priciples goverig the oe-dimesioal discrete radom walk First we review five basic cocepts of probability theory The we cosider the Beroulli
More informationReview of Important Concepts
Appedix 1 Review f Imprtat Ccepts I 1 AI.I Liear ad Matrix Algebra Imprtat results frm liear ad matrix algebra thery are reviewed i this secti. I the discussis t fllw it is assumed that the reader already
More informationLab 11 LRC Circuits, Damped Forced Harmonic Motion
Physics 6 ab ab 11 ircuits, Damped Frced Harmnic Mtin What Yu Need T Knw: The Physics OK this is basically a recap f what yu ve dne s far with circuits and circuits. Nw we get t put everything tgether
More informationEEO 401 Digital Signal Processing Prof. Mark Fowler
EEO 4 Digital Signal Prcessing Pr. ar Fwler DT Filters te Set #2 Reading Assignment: Sect. 5.4 Prais & anlais /29 Ideal LP Filter Put in the signal we want passed. Suppse that ( ) [, ] X π xn [ ] y[ n]
More informationMarkov processes and the Kolmogorov equations
Chapter 6 Markv prcesses ad the Klmgrv equatis 6. Stchastic Differetial Equatis Csider the stchastic differetial equati: dx(t) =a(t X(t)) dt + (t X(t)) db(t): (SDE) Here a(t x) ad (t x) are give fuctis,
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 informationReview of Discrete-time Signals. ELEC 635 Prof. Siripong Potisuk
Review of Discrete-time Sigals ELEC 635 Prof. Siripog Potisuk 1 Discrete-time Sigals Discrete-time, cotiuous-valued amplitude (sampled-data sigal) Discrete-time, discrete-valued amplitude (digital sigal)
More information6.003 Homework #3 Solutions
6.00 Homework # Solutios Problems. Complex umbers a. Evaluate the real ad imagiary parts of j j. π/ Real part = Imagiary part = 0 e Euler s formula says that j = e jπ/, so jπ/ j π/ j j = e = e. Thus the
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 informationUnit -2 THEORY OF DILUTE SOLUTIONS
Uit - THEORY OF DILUTE SOLUTIONS 1) hat is sluti? : It is a hmgeus mixture f tw r mre cmpuds. ) hat is dilute sluti? : It is a sluti i which slute ccetrati is very less. 3) Give a example fr slid- slid
More informationChapter 7: The z-transform. Chih-Wei Liu
Chapter 7: The -Trasform Chih-Wei Liu Outlie Itroductio The -Trasform Properties of the Regio of Covergece Properties of the -Trasform Iversio of the -Trasform The Trasfer Fuctio Causality ad Stability
More informationAMS570 Lecture Notes #2
AMS570 Lecture Notes # Review of Probability (cotiued) Probability distributios. () Biomial distributio Biomial Experimet: ) It cosists of trials ) Each trial results i of possible outcomes, S or F 3)
More informationPHYC - 505: Statistical Mechanics Homework Assignment 4 Solutions
PHYC - 55: Statistical Mechaics Homewor Assigmet 4 Solutios Due February 5, 14 1. Cosider a ifiite classical chai of idetical masses coupled by earest eighbor sprigs with idetical sprig costats. a Write
More informationPHYS-3301 Lecture 9. CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I. 5.3: Electron Scattering. Bohr s Quantization Condition
CHAPTER 5 Wave Properties of Matter ad Quatum Mecaics I PHYS-3301 Lecture 9 Sep. 5, 018 5.1 X-Ray Scatterig 5. De Broglie Waves 5.3 Electro Scatterig 5.4 Wave Motio 5.5 Waves or Particles? 5.6 Ucertaity
More information8.0 Negative Bias Temperature Instability (NBTI)
EE650R: Reliability Physics f Naelectric Devices Lecture 8: Negative Bias Temerature Istability Date: Se 27 2006 Class Ntes: Vijay Rawat Reviewed by: Saakshi Gagwal 8.0 Negative Bias Temerature Istability
More informationLecture 6: Phase Space and Damped Oscillations
Lecture 6: Phase Space and Damped Oscillatins Oscillatins in Multiple Dimensins The preius discussin was fine fr scillatin in a single dimensin In general, thugh, we want t deal with the situatin where:
More informationAnalysis of pressure wave dynamics in fuel rail system
It. Jl. f Multiphysics Vlume Number 3 8 3 Aalysis f pressure wave dyamics i fuel rail system Basem Alzahabi ad Keith Schulz Ketterig Uiversity Siemes Autmtive ABSTRACT A mdel f a amplified cmm rail fuel
More informationµ and π p i.e. Point Estimation x And, more generally, the population proportion is approximately equal to a sample proportion
Poit Estimatio Poit estimatio is the rather simplistic (ad obvious) process of usig the kow value of a sample statistic as a approximatio to the ukow value of a populatio parameter. So we could for example
More informationFourier Method for Solving Transportation. Problems with Mixed Constraints
It. J. Ctemp. Math. Scieces, Vl. 5, 200,. 28, 385-395 Furier Methd fr Slvig Trasprtati Prblems with Mixed Cstraits P. Padia ad G. Nataraja Departmet f Mathematics, Schl f Advaced Scieces V I T Uiversity,
More informationChapter 30. Inductance
Chapter 30 nductance 30. Self-nductance Cnsider a lp f wire at rest. f we establish a current arund the lp, it will prduce a magnetic field. Sme f the magnetic field lines pass thrugh the lp. et! be the
More informationcannot commute.) this idea, we can claim that the average value of the energy is the sum of such terms over all points in space:
Che 441 Quatu Cheistry Ntes May, 3 rev VI. Apprxiate Slutis A. Variati Methd ad Huckel Mlecular Orbital (HMO) Calculatis Refereces: Liberles, Ch. 4, Atkis, Ch. 8, Paulig ad Wils Streitweiser, "MO Thery
More informationmx bx kx F t. dt IR I LI V t, Q LQ RQ V t,
Lecture 5 omplex Variables II (Applicatios i Physics) (See hapter i Boas) To see why complex variables are so useful cosider first the (liear) mechaics of a sigle particle described by Newto s equatio
More informationStudy in Cylindrical Coordinates of the Heat Transfer Through a Tow Material-Thermal Impedance
Research ural f Applied Scieces, Egieerig ad echlgy (): 9-63, 3 ISSN: 4-749; e-issn: 4-7467 Maxwell Scietific Orgaiati, 3 Submitted: uly 4, Accepted: September 8, Published: May, 3 Study i Cylidrical Crdiates
More informationDetermining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationPart a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 )
+ - Hmewrk 0 Slutin ) In the circuit belw: a. Find the magnitude and phase respnse. b. What kind f filter is it? c. At what frequency is the respnse 0.707 if the generatr has a ltage f? d. What is the
More informationradians A function f ( x ) is called periodic if it is defined for all real x and if there is some positive number P such that:
Fourier Series. Graph of y Asix ad y Acos x Amplitude A ; period 36 radias. Harmoics y y six is the first harmoic y y six is the th harmoics 3. Periodic fuctio A fuctio f ( x ) is called periodic if it
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 informationA) 0.77 N B) 0.24 N C) 0.63 N D) 0.31 N E) 0.86 N. v = ω k = 80 = 32 m/s. Ans: (32) 2 = 0.77 N
Q1. A transverse sinusidal wave travelling n a string is given by: y (x,t) = 0.20 sin (2.5 x 80 t) (SI units). The length f the string is 2.0 m and its mass is 1.5 g. What is the magnitude f the tensin
More information