Asked by: Spaska Epifani
science physics

Why Fourier series is used in communication engineering?

Last Updated: 2nd May, 2020

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Communication engineering mainly deal withsignalsand hence signals are of various type likecontinues,discrete,periodic,non-periodic and many of many types.NowFourier transform helps us to converted time domainsignalin frequency domain. Because it allows us to extract thefrequencycomponents of a signal.

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Also asked, what is Fourier series used for?

Basically, fourier series is usedtorepresent a periodic signal in terms of cosine andsinewaves.

Subsequently, question is, why do we use Fourier series and Fourier transform? The Fourier series is used to represent aperiodicfunction by a discrete sum of complex exponentials, whiletheFourier transform is then used to represent ageneral,nonperiodic function by a continuous superposition orintegral ofcomplex exponentials.

Subsequently, one may also ask, why Fourier transform is used in communication?

In the theory of communication a signalisgenerally a voltage, and Fourier transform isessentialmathematical tool which provides us an inside view ofsignal andits different domain, how it behaves when it passesthrough variouscommunication channels, filters, andamplifiers and it alsohelp in analyzing various

What are the types of Fourier series?

Four different forms of Fourier transform.Allpreviously discussed Fourier series expansionsandtransforms of various types of signals (periodic,aperiodic,continuous, discrete) can be considered as differentforms(special cases) of the same Fourier transform,and therebyunified.

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What are the two types of Fourier series?

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What is Fourier series and its applications?

A Fourier (pronounced foor-YAY) series isaspecific type of infinite mathematical seriesinvolvingtrigonometric functions. Fourier series are used inappliedmathematics, and especially in physics and electronics, toexpressperiodic functions such as those that comprisecommunicationssignal waveforms.

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What is Fourier's Theorem?

Fourier theorem states that a periodicfunctionf(x) which is reasonably continuous may be expressed as thesum ofa series of sine or cosine terms (called theFourierseries), each of which has specific amplitude andphasecoefficients known as Fouriercoefficients.

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What are the advantages of Fourier transform?

Advantages. The main advantage ofFourieranalysis is that very little information is lost fromthe signalduring the transformation. The Fouriertransformmaintains information on amplitude, harmonics, andphase and usesall parts of the waveform to translate the signalinto thefrequency domain.

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What is Fourier transform and its properties?

The Fourier transform (FT) decomposes afunctionof time (a signal) into its constituent frequencies.Theterm Fourier transform refers to both the frequencydomainrepresentation and the mathematical operation that associatesthefrequency domain representation to a function oftime.

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What are FFT used for?

Igor uses the Fast Fourier Transform(FFT)algorithm to compute a Discrete Fourier Transform(DFT). TheFFT can be used to simply characterize themagnitudeand phase of a signal, or it can be used incombination withother operations to perform more involvedcomputations such asconvolution or correlation.

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How does fourier transform work?

It takes two signals and puts them together to make anewsignal. The Fourier transform returns a representationof asignal as a superposition of sinusoids. Fouriertransformsare used to perform operations that are easy toimplement orunderstand in the frequency domain, such asconvolution andfiltering.

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What do you mean by Fourier transform?

A Fourier transform is a mathematicaltechniquefor converting a time function into one expressed in termsoffrequency. A Fourier transform is a circuitanalysistechnique that decomposes or separates a waveform orfunction intosinusoids of different frequency which sum to theoriginalwaveform.

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Why does Gibbs phenomenon occur?

Gibbs' phenomenon occurs near ajumpdiscontinuity in the signal. It says that no matter how manytermsyou include in your Fourier series there will always be anerror inthe form of an overshoot near the discontinuity.

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Can any function be represented as a Fourier series?

Any function that is defined over the entirerealline can be represented by a Fourierseries ifit is periodic.

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Who discovered Fourier series?

The Fourier series is named in honourofJean-Baptiste Joseph Fourier (1768–1830), whomadeimportant contributions to the study oftrigonometricseries, after preliminary investigations byLeonhard Euler,Jean le Rond d'Alembert, and DanielBernoulli.

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What is exponential Fourier series?

Fourier Series at a Glance
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What is the difference between Laplace transform and Fourier transform?

The Laplace transform is similar to theFouriertransform. While the Fourier transform of afunction is acomplex function of a real variable (frequency), theLaplacetransform of a function is a complex function of acomplexvariable. Laplace transforms are usually restrictedtofunctions of t with t ≥ 0.

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What is time domain and frequency domain?

Put simply, a time-domain graph shows howasignal changes over time, whereasafrequency-domain graph shows how much of thesignallies within each given frequency band over a rangeoffrequencies. The "spectrum" of frequencycomponentsis the frequency-domain representation ofthesignal.