matlab code for discrete time fourier series

... Trong miền tần số: phương pháp Fourier Transform. - Trong miền thời gian và tần số: STFT( Short Time Fourier Transform). 2.4.1. Phương pháp Fourier: 2.4.1.1. Biến đổi Fourier: Cho một hàm f(t) ... kết thúc của sự kiện thì Fourier không phát hiện được. 2.4.2. Phương pháp STFT: Để đạt được một biến đổi Fourier cục bộ, chúng ta có thể định nghĩa một biến đổi Fourier cửa sổ. Tín hiệu đầu ... đổi Fourier của nó được định nghĩa: () () () tfedtetfF titj , ωω ω == ∫ ∞ ∞− − (2.14) Biến đổi Fourier ngược là: () () ∫ ∞ ∞− = ωω π ω deFtf tj 2 1 (2.15) Giả sử rằng biến đổi Fourier...

... as its domain. A discrete time, continuous amplitude signal has R as its range. A discrete time, discrete amplitude signal has Z as its range. Here, the focus is on discrete time signals. Quantization ... maps the finite set of discrete time, continuous amplitude signals into a finite set of discrete time, discrete amplitude signals. A signal x(n) is quantized one block at a time in that p (almost ... collection C is called the codebook and the number of vectors in the codebook, N, is known as the codebook size. The entries of the codebook are known as codewords or codevectors. If p = 1, we...

... configured for RSVP. Configure CODEC and VAD for Dial Peers Coder-decoder (CODEC) and voice activity detection (VAD) for a dial peer determine how much bandwidth the voice session uses. CODEC typically ... Voice over IP for the Cisco 3600 Series VC-13 Configuring Voice over IP for the Cisco 3600 Series This chapter shows you how to configure Voice over IP (VoIP) on the Cisco 3600 series. For a description ... over IP for it to run smoothly over Frame Relay. For example, a public Frame Relay cloud provides no guarantees for QoS. Refer to the “Configure Frame Relay for Voice over IP” section for information...

... Laplace and Z Transforms Laplace transforms are an important tool for analysis of continuous time dynamic systems, and Z transforms are an important tool for analysis of discrete time dynamic systems. ... listed here. fft(x) Compute the discrete Fourier transform of the vector x ifft(x) Compute the inverse discrete Fourier transform of the vector x fftshift Shifts the fft output from the discrete range frequency ... commands helpful for calculating and plotting frequency response given the system function for continuous or discrete time systems as ratios of polynomials. bode(n,d) Plot the Bode diagram for a CT system...

... displacements a ã For each element, evaluate the strains and stresses (post-processing) 2.5 First problem and first MATLAB code To illustrate some of the basic concepts, and introduce the first MATLAB code, we ... q (e) represents the vector of nodal forces. If the element undergoes the action of distributed forces, it is necessary to transform those forces into nodal forces, by q (e) = k (e)  1 −1 −11   u (e) 1 u (e) 2  − (bl) (e) 2  1 1  = ... is E =30e6, and the area of the cross-section is A =1. The code problem2.m considers an isoparametric formulation. % % MATLAB codes for Finite Element Analysis ...

... TCON Timer Control Receiver Register |TF1|TR1|TF0|TR0| | | | | <-Timer Controls><-Unused for timers TRx Timer x run control 0 = Timer not running 1 = Timer running ... waveforms in Fig 1 show the waveform on a single conductor to transmit a byte (0x41) serially. The upper waveform is the TTL-level waveform seen at the transmit pin of 8051. The lower waveform ... true with the 8051, which has separate memory spaces for code, on-chip data, and external data. To accommodate for this when writing C code, Keil added extensions to variable declarations...

... PropertiesoftheDiscreteTimeFourierTransform BecausetheDTFTisacloserelativeoftheclassicalCTFouriertransformitshouldcomeasnosurprise thatmanypropertiesoftheDTFTaresimilartothosepresentedfortheCTFouriertransforminthe previoussection.Infact,formanyofthepropertiespresentedearlierananalogouspropertyexists fortheDTFT.ThefollowinglistparallelsthelistthatwaspresentedintheprevioussectionfortheCT Fouriertransform,totheextentthatthesamepropertyexists.AmorecompletelistofDTFTpairsis giveninTable1.4.(Notethattheprimednotationonω  isdroppedinthefollowingtosimplifythe notation,andtobeconsistentwithstandardusage.) 1.Linearity(superposition):DTFT{af 1 [n]+bf 2 [n]}=aDTFT{f 1 [n]}+bDTFT{f 2 [n]} (aandb,complexconstants) 2.Indexshifting:DTFT{f[n−n 0 ]}=e −jωn 0 DTFT{f[n]} 3.Frequencyshifting:e jω 0 n f[n]=DTFT −1 {F(e j(ω−ω 0 ) )} 4.Timedomainconvolution:DTFT{f 1 [n]∗f 2 [n]}=DTFT{f 1 [n]}DTFT{f 2 [n]} 5.Frequencydomainconvolution:DTFT{f 1 [n]f 2 [n]}=(1/2π)DTFT{f 1 [n]}∗DTFT{f 2 [n]} 6.Frequencydifferentiation:nf[n]=DTFT −1 {dF(e jω )/dω} Notethatthetime-differentiationandtime-integrationpropertiesoftheCTFTdonothaveanalogous counterpartsintheDTFTbecausetimedomaindifferentiationandintegrationarenotdefinedforDT c  1999byCRCPressLLC ... tationhasbothamagnitudeandaphasespectrum.Forexample,themagnitudeofthea n isplotted inFig.1.4forthesawtoothwaveformofFig.1.3.Thefactthatthea n constituteadiscretesetis consistentwiththefactthataperiodicsignalhasa“linespectrum,”i.e.,thespectrumcontainsonly integermultiplesofthefundamentalfrequencyω 0 .Therefore,theequationpairgivenby(1.5a) and(1.5b)canbeinterpretedasatransformpairthatissimilartotheCTFouriertransformfor periodicsignals.ThisleadstotheobservationthattheclassicalFourierseriescanbeinterpreted asaspecialtransformthatprovidesaone-to-oneinvertiblemappingbetweenthediscrete-spectral domainandtheCTdomain.Thenextsectionshowshowtheperiodicityconstraintcanberemoved toproducethemoregeneralclassicalCTFouriertransform,whichappliesequallywelltoperiodic andaperiodictimedomainwaveforms. FIGURE1.3:PeriodicCTsignalusedinFourierseriesexample. FIGURE1.4:MagnitudeoftheFouriercoefficientsforexampleofFigure1.3. 1.2.2 TheTrigonometricFourierSeries AlthoughFourierseriesexpansionsexistforcomplexperiodicsignals,andFouriertheorycanbe generalizedtothecaseofcomplexsignals,thetheoryandresultsaremoreeasilyexpressedforreal- valuedsignals.Thefollowingdiscussionassumesthatthesignals(t)isreal-valuedforthesakeof simplifyingthediscussion.However,allresultsarevalidforcomplexsignals,althoughthedetailsof thetheorywillbecomesomewhatmorecomplicated. Forreal-valuedsignalss(t),itispossibletomanipulatethecomplexexponentialformoftheFourier seriesintoatrigonometricformthatcontainssin(ω 0 t)andcos(ω 0 t)termswithcorrespondingreal- c  1999byCRCPressLLC ... (1.14b) Thesetofallvaluesofuforwhichtheintegralof(1.14b)convergesiscalledtheregionofconvergence (ROC).BecausethetransformS(u)isdefinedonlyforvaluesofuwithintheROC,thepathof integrationin(1.14a)mustbedefinedbyσsothattheentirepathlieswithintheROC.Insome literaturethistransformpairiscalledthebilateralLaplacetransformbecauseitisthesameresult obtainedbyincludingboththenegativeandpositiveportionsofthetimeaxisintheclassicalLaplace transformintegral.[Notethatin(1.14a)thecomplexfrequencyvariablewasdenotedbyurather thanbythemorecommons,inordertoavoidconfusionwithearlierusesofs(·)assignalnotation.] ThecomplexFouriertransform(bilateralLaplacetransform)isnotoftenusedinsolvingpractical problems,butitssignificanceliesinthefactthatitisthemostgeneralformthatrepresentsthepoint atwhichFourierandLaplacetransformconceptsbecomethesame.Identifyingthisconnection reinforcesthenotionthatFourierandLaplacetransformconceptsaresimilarbecausetheyarederived byplacingdifferentconstraintsonthesamegeneralform. 1.4 TheDiscreteTimeFourierTransform ThediscretetimeFouriertransform(DTFT)canbeobtainedbyusingtheDTsamplingmodeland consideringtherelationshipobtainedin(1.12)tobethedefinitionoftheDTFT.LettingT=1so thatthesamplingperiodisremovedfromtheequationsandthefrequencyvariableisreplacedwith c  1999byCRCPressLLC ...

... for calclulating a kind Stochastic Mixed LQR/H ∞ Control for Linear Discrete- Time Systems http://dx.doi.org/10.5772/51019 5 Chapter 1 Stochastic Mixed LQR/H ∞ Control for Linear Discrete- Time ... problem) for linear discrete- time systems with uncertainty was presented. When the parameter uncertainty equals zero, the discrete- time state feedback mixed QGC/H ∞ control problem reduces to the discrete- time ... problem for linear discrete- time systems (de Souza & Xie 1992), H ∞ control problem for linear continuous -time systems (Gadewadikar et al. 2007), mixed LQR/H ∞ con‐ trol problem for linear...

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