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[PDF] 3-4 Fourier Series

8 sept 2012 · This is the mathematical theory of Fourier series which uses the periodic waveforms, such as square waves, triangle waves, rectified sinusoids, and so on simple property of the complex exponential signal—the integral of a The mathematical formula for the full-wave rectified sine signal is just the 

[PDF] Fourier Series

Fourier Series: Half-wave Rectifier • Ex A sinusoidal voltage Esinωt, is passed through a half-wave rectifier that clips the negative portion of the wave Find the

[PDF] Chapter 16 The Fourier Series

It is also useful to know the values of the cosine, sine, and exponential functions for Determine the Fourier series for the half-wave rectified cosine function

fourier series - gulden kokturks home page

4 jui 2010 · What is the conditions of Fourier series expansion for a signal? Answer: Exponential Fourier series DEU, Electrical Half-wave Symmetry; If a signal has an half wave symmetry, only Full-wave rectifier DEU, Electrical 

[PDF] Fourier series coefficients for a rectified sine wave

The period of the sinusoid (inside the absolute value symbols) is T1 = 2π/ω1 The period of the rectified sinusoid is one half of this, or T = T1/2 = π/ω1 Therefore,

[PDF] Half-Wave Rectifier - Zenon Bank

Vm / , so the rms value of a half-wave rectified sine wave is Vrms If periodic voltage and current waveforms represented by the Fourier series case), the exponential term in equation 3 1 becomes very small compared to unity and the diode

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Q2 Fourier series of the output voltage of an ideal full-wave Diode Rectifier The following circuit is an ideal full-wave rectifier It is often used as a first stage to

[PDF] 1 Experiment 1 Spectral Analysis 1 Objectives: • To investigate the

1 5 cos(1000 )t Figure (1) 2 (a) Find the exponential Fourier series expansion for the time-shifted version of the halfwave rectified sinusoidal signal: y (t) = x2(t 

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Problem 10: Show that the exponential form of a Fourier series representation of a function ( ) f x through a half-wave rectifier, which clips the negative portion 

[PDF] exponential fourier series of square wave

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FOURIER SERIES

DEU, Electrical and Electronics Eng. 6.04.2010

Contact Information

Phone:4127165

E-mail:gulden.kokturk@deu.edu.tr

Webpage:gulden.kokturk.com

Office Hours for This Module

April,5-9:Wendesday3-4,Friday5-6

April,12-16:Wendesday3-4,Thursday3-4

DEU, Electrical and Electronics Eng. 6.04.2010

yWhatisthemeaningoftheFourierSeries? amathematicaltoolforsignalanalysis. yFourierserieswerefoundedbyJosephFourier whenhewasinvestigatedheatvariationsona circularmetal. signal,yoursignalmustprovidesome conditions.

DEU, Electrical and Electronics Eng. 6.04.2010

forasignal?

Answer:

DRICHLET CONDITIONS

DEU, Electrical and Electronics Eng. 6.04.2010

Drichlet Conditions

asingleperiodT.So, finiteforanyfiniteperiodoftime. functionf(t)foranyfiniteperiodoftime.

DEU, Electrical and Electronics Eng. 6.04.2010

Fourier Series

yTrigonometricFourierseries yExponentialFourierseries

DEU, Electrical and Electronics Eng. 6.04.2010

Trigonometric Fourier Series

Ifasignalhasaperiodicwaveform,itcanbe

explainedasaseriesofharmonicallyrelated sinusoids.Ithasafundamentallyfrequencyor firstharmonic.

Conventionally,aperiodicsignalf(t)as

ThefirsttermisaconstantandrepresentsDC

componentofthesignal.

DEU, Electrical and Electronics Eng. 6.04.2010

property.

Fromtheseequations;

DEU, Electrical and Electronics Eng. 6.04.2010

If m is equal to n, then

DEU, Electrical and Electronics Eng. 6.04.2010

Forsimplicity,weassumethatȦ=1.Then

withsin2t.

Afterthatmultiplyingtermsofbothsidesbywe

integratetheperiodfrom0to2ʌ.

DEU, Electrical and Electronics Eng. 6.04.2010

Then

DEU, Electrical and Electronics Eng. 6.04.2010

The coefficients a0, an and bn

DEU, Electrical and Electronics Eng. 6.04.2010

Symmetry in Trigonometric Fourier Series

Types of Symmetry

Oddfunction;f(-t)=-f(t)

Evenfunction;f(-t)=f(t)

symmetry,onlyodd(oddcosineandoddsine)

DEU, Electrical and Electronics Eng. 6.04.2010

Half-Wave Symmetry

yAnyperiodicsignalwithperiodTis expressedmatematicallyasf(t)=f(t+T). byf(t)=f(t+T/2). yThemeaningoftheaboveequation; theshapeofthenegativecycleofthesignal isthesameasthepositivehalfcycle.

DEU, Electrical and Electronics Eng. 6.04.2010

Examples

FS.1.

DEU, Electrical and Electronics Eng. 6.04.2010

FS.2.

DEU, Electrical and Electronics Eng. 6.04.2010

FS.3.

DEU, Electrical and Electronics Eng. 6.04.2010

FS.4. Half-wave rectifier

DEU, Electrical and Electronics Eng. 6.04.2010

FS.5. Full-wave rectifier

DEU, Electrical and Electronics Eng. 6.04.2010

Exponential Fourier Series

yAsignalisexpressedinanexponentialform. istoneedlessintegration.Wemustcalculate trigonometricFourierseries.Howeverin exponentionalform,wemusttakeonlyone integration.

DEU, Electrical and Electronics Eng. 6.04.2010

formforthesignalf(t)asfollows: ySubstitutingtermsof intof(t). yGroupingtermswithsameexponents

DEU, Electrical and Electronics Eng. 6.04.2010

yTerms in paranthesis are represented by yRemember that Cncoefficents are coplex. yMultiplyingbothsidesoff(t)withand integratingoveroneperiod.

Forsimplicity,weassumethatȦ=1.

DEU, Electrical and Electronics Eng. 6.04.2010

yBecause of

Weobservethattherightsideofthe

aboveequationarezerooutofthelast term.Then

DEU, Electrical and Electronics Eng. 6.04.2010

In general, .

or

Fourierseriesfromcoefficientsofthe

exponententialFourierseries.

DEU, Electrical and Electronics Eng. 6.04.2010

Symmetry in Exponential Fourier Series

Sinceevenfunctionshaveonlycosineterms.

Oddfunction;f(-t)=-f(t)

evenfunctionshavenocosineterms,onlysine terms.

Evenfunction;f(-t)=f(t)

yIfthereisahalf-wavesymmetry,Cn=0for n=even. yIfthereisnosymmetry,thesignalf(t)is complex.

DEU, Electrical and Electronics Eng. 6.04.2010

Examples

FS.6.

DEU, Electrical and Electronics Eng. 6.04.2010

Examples

FS.7.

DEU, Electrical and Electronics Eng. 6.04.2010

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