discrete fourier series matlab

... decomposed. Chapter 8- The Discrete Fourier Transform 145 Type of Transform Example Signal Fourier Transform Fourier Series Discrete Time Fourier Transform Discrete Fourier Transform signals that ... from negative to positive infinity. This class of Fourier Transform is sometimes called the Discrete Fourier Series, but is most often called the Discrete Fourier Transform. You might be thinking that ... Fourier decomposition, the heart of the DFT. The Family of Fourier Transform Fourier analysis is named after Jean Baptiste Joseph Fourier (1768-1830), a French mathematician and physicist. (Fourier...

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Ngày tải lên: 24/12/2013, 12:16

... ConvergenceoftheFourierSeries TheFourierseriesrepresentationofaperiodicsignalisanapproximationthatexhibitsmeansquared convergencetothetruesignal.Ifs(t)isaperiodicsignalofperiodT,ands  (t)denotestheFourier seriesapproximationofs(t),thens(t)ands  (t)areequalinthemeansquaresenseif MSE=  T/2 −T/2 |s(t)−s(t)  | 2 dt=0 ... analogous to the classical Fourier (CT) transform, and the DFT is analogous to the classical (CT) Fourier series. 1.7 Selected Applications of Fourier Methods 1.7.1 Fast Fourier Transform in Spectral ... (1.7) Evenwith(1.7)satisfied,meansquareerror(MSE)convergencedoesnotmeanthats(t)=s  (t) ateveryvalueoft.Inparticular,itisknownthatatvaluesoft,wheres(t)isdiscontinuous,the Fourierseriesconvergestotheaverageofthelimitingvaluestotheleftandrightofthediscontinuity. Forexample,ift 0 isapointofdiscontinuity,thens  (t 0 )=[s(t − 0 )+s(t + 0 )]/2,wheres(t − 0 )and s(t + 0 )weredefinedpreviously.(Notethatatpointsofcontinuity,thisconditionisalsosatisfiedby thedefinitionofcontinuity.)BecausetheDirichetconditionsrequirethats(t)haveatmostafinite numberofpointsofdiscontinuityinoneperiod,thesetS t ,definedasallvaluesoftwithinone periodwheres(t)=s  (t),containsafinitenumberofpoints,andS t isasetofmeasurezerointhe formalmathematicalsense.Therefore,s(t)anditsFourierseriesexpansions  (t)areequalalmost everywhere,ands(t)canbeconsideredidenticaltos  (t)fortheanalysisofmostpracticalengineering problems. Convergencealmosteverywhereissatisfiedonlyinthelimitasaninfinitenumberoftermsare includedintheFourierseriesexpansion.IftheinfiniteseriesexpansionoftheFourierseriesis truncatedtoafinitenumberofterms,asitmustbeinpracticalapplications,thentheapproximation willexhibitanoscillatorybehavioraroundthediscontinuity,knownastheGibbsphenomenon[1]. Lets  N (t)denoteatruncatedFourierseriesapproximationofs(t),whereonlythetermsin(1.5a) fromn=−Nton=NareincludedifthecomplexFourierseriesrepresentationisused,orwhere onlythetermsin(1.6a)fromn=0ton=NareincludedifthetrigonometricformoftheFourier seriesisused.Itiswellknownthatinthevicinityofadiscontinuityatt 0 theGibbsphenomenon causess  N (t)tobeapoorapproximationtos(t).ThepeakmagnitudeoftheGibbsoscillationis13% ofthesizeofthejumpdiscontinuitys(t − 0 )−s(t + 0 )regardlessofthenumberoftermsusedinthe approximation.AsNincreases,theregionthatcontainstheoscillationbecomesmoreconcentrated intheneighborhoodofthediscontinuity,until,inthelimitasNapproachesinfinity,theGibbs oscillationissqueezedintoasinglepointofmismatchatt 0 . Ifs  (t)isreplacedbys  N (t)in(1.7),itisimportanttounderstandthebehavioroftheerrorMSE N asafunctionofN,where MSE N =  T/2 −T/2 |s(t)−s  N (t)| 2 dt...

Ngày tải lên: 27/01/2014, 03:20

... general Maclaurin series gives cos(θ)= ∞  n=0 f (n) (0) n! θ n = ∞  n≥0 n even (−1) n/2 n! θ n sin(θ)= ∞  n≥0 n odd (−1) (n−1)/2 n! θ n DRAFT of “Mathematics of the Discrete Fourier Transform ... practical spectrum analysis exam- ples, using primarily Matlab to analyze and display signals and their spectra. DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O. Smith, CCRMA, ... not just an integer. 2.6 Numerical Tools in Matlab In Matlab, root-finding is always numerical: 3 >> % polynomial = array of coefficients in Matlab >> p = [1 0 0 0 5 7]; % p(x) = x^5...

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... cosines of whole multiples of x, that is series of the form b 0 + b 1 cos x + b 2 cos 2x + ··· + a 1 sin x + a 2 sin 2x + ··· are generally known as Fourier s series. Let us endeavor to develop a ... 2) 9 This equation was first studied by Fourier in considering the cooling of a cylinder. We shall designate it as Fourier s Equation.” DEVELOPMENT IN TRIGONOMETRIC SERIES. 32 Multiply the first equation ... convergence of the series (1), for which we have not space, entirely confirms the result formulated above 2 and shows in addition that at a point of finite discontinuity the series has a value...

Ngày tải lên: 15/03/2014, 00:20

... When we use MATLAB, its canon() function returns a companion matrix which is the transpose of A in (4-19); this form is called the observable canonical form. We shall see that in MATLAB Session ... Taylor series expansion on the exponential function of A, and evaluate the state transition matrix with Φ(t) = e At =I+At+ 1 2! A 2 t 2 + 1 3! A 3 t 3 + (4-14) Instead of an infinite series, ... transfer function is not as bad, as long as t d « τ. How do you plot the exact solution in MATLAB? 10. Use MATLAB to observe the effect of higher order multicapacity models as in Example 3.3. Try...

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... >>save('C:\matlabR12\work\ten_file') %lu ton bộ biến trong Workspace >>save('C:\matlabR12\work\ten_file', 'x','y')% chỉ lu biến x v y Chú ý: C:\matlabR12\work\ten_file ... (- Tungvn40@yahoo.com CM Soft 70 NCT F2 Q10 Trang 3 1.1.4 Lm quen với matlab Trớc tiên để khởi động MATLAB bạn kích đúp (hoặc đơn) v biểu tợng file MATLAB. exe ,trên mn hình xuất hiện cửa sổ sau.( Xem hình ... 1.2246e-016 + Các phép tính sử dụng trong Matlab : Trong MATLAB cũng sử dụng các phép toán thông thờng đợc liệt kê trong bảngsau Ký tự ý nghĩa Lệnh Matlab + Cộng a + b a+b - Trừ a - b a-b...

Ngày tải lên: 16/08/2012, 14:41

Ngày tải lên: 16/08/2012, 15:29

... Hình 5.1 path browser trong MATLAB 5.2 Hình 5.1 path browser trong MATLAB 5.2Hình 5.1 path browser trong MATLAB 5.2 Hình 5.1 path browser trong MATLAB 5.2 Cửa sổ path browser path ... browserpath browser path browser trong MATLAB 5.0 không khác lắm so với MATLAB 5.2, chủ yếu là các nút thay đổi đờng dẫn trong MATLAB 5.2 thì nó đặt ở trên đỉnh còn ở MATLAB 5.0 nó đợc đặt ở bên phải. ... hình hiển thị C: \MATLAB là th mục đích mặc định của quá trình cài đặt. Nếu bạn muốn cài đặt vào th mục khác hoặc đổi tên th mục thì bạn lựa chọn Browse. MATLAB cho Macintosh. MATLAB cho máy...

Ngày tải lên: 28/08/2012, 11:00