# What is the history of fourier series?

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It is quite complicated, and starts before Fourier. Trigonometric series arose in problems connected with astronomy in the 1750s, and were tackled by Euler and others. In a different context, they arose in connection with a vibrating string (e.g. a violin string) and solutions of the wave equation.

Still in the 1750s, a controversy broke out as to what curves could be represented by trigonometric series and whether every solution to the wave equation could be represented as the sum of a trigonometric series; Daniel Bernoulli claimed that every solution could be so represented and Euler claimed that arbitrary curves could not necessarily be represented. The argument rumbled on for 20 years and dragged in other people, including Laplace. At that time the concepts were not available to settle the problem.

Fourier worked on the heat equation (controlling the diffusion of heat in solid bodies, for example the Earth) in the early part of the 19th century, including a major paper in 1811 and a book in 1822. Fourier had a broader notion of function than the 18th-century people, and also had more convincing examples.

Fourier's work was criticised at the time, and his insistence that discontinuous functions could be represented by trigonometric series contradicted a theorem in a textbook by the leading mathematician of the time, Cauchy.

Nonetheless Fourier was right; Cauchy (and Fourier, and everyone else at that time) was missing the idea of uniform convergence of a series of functions. Fourier's work was widely taken up, and also the outstanding problems (just which functions can be represented by Fourier series?; how different can two functions be if they have the same Fourier series?) were slowly solved.

Source: Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972, pages 478-481, 502-514, 671-678,and 964.
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# What is the difference between a Fourier series and a Fourier transform?

The Fourier series is an expression of a pattern (such as an electrical waveform or signal) in terms of a group of sine or cosine waves of different frequencies and amplitude. This is the frequency domain. The Fourier transform is the process or function used to convert from time domain (example: ( Full Answer )

# What is a fast Fourier transform?

A fast Fourier transform is an efficient algorithm for working out the discrete Fourier transform - which itself is a Fourier transform on 'discrete' data, such as might be held on a computer. Contrast this to a 'continuous Fourier transform' on, say, a curve. One would need an infinite amount of da ( Full Answer )

# What are the applicaton of fourier series?

It can be used in function approximation, especially in physics and numerical analysis and system & signals. Actually, the essence is that the basis of series is orthorgonal.

# Difference between fourier series and z-transform?

z transform is related to discrete time signal while fourier series is related to continuous time signal. z transform=sigmalm -infinty to +infinity x(n)z-n

# What is Fourier transformation?

Fourier transform. It is a calculation by which a periodic function is split up into sine waves.

# What is the difference between fourier series and discrete fourier transform?

Fourier series is the sum of sinusoids representing the given function \nwhich has to be analysed whereas discrete fourier transform is a function which we get when summation is done.

# What did Joseph fourier discover?

Joseph Fourier is a French mathematician and physicist. Fourier isgenerally credited with the discovery of the greenhouse effect.

# What is fourier analysis?

Fourier analysis began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions. The attempt to understand functions (or other objects) by breaking them into basic pieces that are easier to understand is one of the central themes in ( Full Answer )

# What is fourier series?

Consider a periodic function, generally defined by f(x+t) = f(x) for some t. Any periodic function can be written as an infinite sum of sines and cosines. This is called a Fourier series.

# What is the Fourier Transform?

The Fourier transform is a mathematical transformation used totransform signals between time or spatial domain and frequencydomain. It is reversible. It refers to both the transform operationand to the function it produces.

# Who is Joseph fourier?

Joseph Fourier was a French mathematician and Physicist. He hasworked on the subject of heat transfer and vibrations and alsocredited with discovery of green house effect.

# Difference between fourier series fourier transform discrete time fourier transform and DFT?

A Fourier series is a series of sine and cosine harmonics of a particular frequency. For example sinf+icosf + 3 sin2f+ 5icos2f... where the successive terms are multiples of the fundamental frequency f. It is typical ( but as far as I know not required) that complex numbers are used. A Fourier tran ( Full Answer )

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That was Jack Quinn of the 1930 Philadelphia Athletics. Quinn pitched 2 innings in Game 3 of the 1930 World Series at the age of 47 years, 3 months, 3 days. Quinn was born July 1, 1883 and Game 3 was played October 4, 1930.

# What is the application of Fourier series in civil engineering?

when we have need to know the temperature in a bar about any distance we can use fourier series to know that and then we can apply sufficient temperature.

# Difference between fourier transform and first fourier transform?

The question almost certainly intends "fast" instead of "first". The difference between a Fourier Transform and a Fast Fourier Transform is only the amount of effort required to generate the result. Both have the same the result. The original Fourier Transform requires an amount of effort which is p ( Full Answer )

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# In Fourier transformation and Fourier series which one follows periodic nature?

\nThe Fourier series can be used to represent any periodic signal using a summation of sines and cosines of different frequencies and amplitudes. Since sines and cosines are periodic, they must form another periodic signal. Thus, the Fourier series is period in nature.\n. \nThe Fourier series is ( Full Answer )

# What is the fourier series?

It's an infinite sum of sines and cosines that can be used to represent any analytic (well-behaved, like without kinks in it) function.

# Can a discontinuous function be developed in the fourier series?

\nyes it can, if you know how to use or have mathematica have a look at this demo\n. \nhttp://demonstrations.wolfram.com/ApproximationOfDiscontinuousFunctionsByFourierSeries/

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# What did Charles Fourier do?

He was a philosopher who wanted to become an engineer before. He served in the French Army and also worked as a clerk in lyon witch is when he wrote his first major paper. During the Industrial Revolution he assited by arguing in his book "Theory of Four Movements" that the liberty of women and the ( Full Answer )

# Can a discontinuous function be developed in a Fourier series?

Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.

# What is the importance of fourier series?

The Fourier series is important because it allows one to model periodic signals as a sum of distinct harmonic components. In other words, representing signals in this way allows one to see the harmonics in a signal distinctly, which makes it easy to see what frequencies the signal contains in order ( Full Answer )

# Why fourier series is used for frequency domain?

The fourier series relates the waveform of a periodic signal, in the time-domain, to its component sine/cosine frequency components in the frequency-domain. You can represent any periodic waverform as the infinite sum of sine waves. For instance, a square wave is the infinite sum of k * sin(k thet ( Full Answer )

# What are the application of Fourier series?

any signal can be represented by sum of sine and cosine signals...when fs is applied to a signal it is represented by a function containing only sine and cosine signals...mixing 2 signals produces a diff 1..like tat wen sine and cosine is mixed a diff required signal is produced.. a o/2 +summation ( Full Answer )

# What happen when fourier series is taken over asignal?

You use the fourier series to convert a signal from the time domain into the frequency domain, and vice versa. This is done by computing the sine waves that would be required to create the original signal. When done, you get a spectrogram, showing the intensity of each frequency (frequency domain) ( Full Answer )

# How does the graph of Fourier Series differ to the graph of Fourier Transform?

You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,... Also, the fourier series will have a limited domain corresponding to ( Full Answer )

# Who has the most hits in World Series history?

Yogi Berra with 71. Berra played in 14 World Series with the New York Yankees between 1947-1963.

# Can every function be expanded in fouriers series?

no every function cannot be expressed in fourier series... fourier series can b usd only for periodic functions.

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# What is the practical application of a Fourier series?

There are many applications for this complex theory. One of these include the determination of harmonic components in a complex waveform. This is very helpful in analyzing AC waveforms in Electrical Engineering.

# Why cannot aperiodic signal be represented using fourier series?

An aperiodic signal cannot be represented using fourier series because the definition of fourier series is the summation of one or more (possibly infinite) sine wave to represent a periodic signal. Since an aperiodic signal is not periodic, the fourier series does not apply to it. You can come clo ( Full Answer )

# What was the longest game in World Series history?

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# What is the difference between fourier series and fourier transform?

As it has been already hinted, Fourier Series is used for periodic signals. It represents the signal by the discrete-time sequence of basis functions with finite and concrete amplitude and phase shift. The basis functions, according to the theory, are harmonics with the frequencies, divisible by the ( Full Answer )

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Terry Deary. I love Horrible Histories, so I should know, even if no-one else does!! I'm only 11 too!!

# Where fourier series are used in real life?

Fourier analysis is used in many places. Three examples are digital filtering, where a signal is converted to frequency domain, certain bands are removed or processed, and then converted back to time domain; your cell phone or its headset, if it has advanced noise cancellation technology; and the te ( Full Answer )

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Yes, there will be, it starts next spring, spring 2012. Mathew Baynton will be in series 4, as will Ben Willbond, Jim Howick and Larry Rickard, so will Martha Howe-Douglas and Dominique Moore.

# What did fourier invent?

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# Why don't you use fourier series for analog signals?

Fourier Series Operations are done on Neumeric Set of Data. Analog Signals inherently are Not in the Neumeric Domain. So it is Not Possible to Do any Fourier Operations directly on such Signals. In the purely Analog World , some equivalent operations are done using Passive Networks of Resistors ( Full Answer )

# What is the practical application of fourier series in electrical engineering?

In electrical engineering, the Fourier series is used to analysesignal waveforms to find their frequency contest. This is needed todesign communication systems that will deliver the signal to thereceiver in good shape. If you go on to study the next step, the Fourier Transform, that isreally interes ( Full Answer )

# What is the Fourier Series for x sinx from -pi to pi?

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# In Mathematics what is meant by the Fourier series?

The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.

# What is the real time application for fourier series in signals?

Fourier series analysis is useful in signal processing as, byconversion from one domain to the other, you can apply filters to asignal using software, instead of hardware. As an example, you canbuild a low pass filter by converting to frequency domain, choppingoff the high frequency components, and ( Full Answer )

# What is the difference between fourier series and fourier transform with real life example please?

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# Find the Fourier series of the periodic function f sin x 0 x l -2 L-l?

Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "divided by", "equals".