# What is the history of fourier series?

# 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:… voltage samples over time, as you see on an oscilloscope) to the frequency domain, which you see on a graphic equalizer or spectrum analyzer. The inverse Fourier transform converts the frequency domain results back to time domain. The use of transforms is not limited to voltages. ( 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…ta points to truly represent a curve, something that cannot be done with a computer. .
Check out: The Scientist And Engineer's Guide To Digital Signal Processing . It is a free, downloadable book that deals, inter alia , with Fourier transforms; chapters 8-12 are germane to your question. This is a highly practical, roll-yer-sleeves-up book for, as the title says, scientists and engineers, but Smith describes the underlying theory well. The sample code supplied with the book is in BASIC and FORTRAN, of all things; the author does this for didactic purposes to make the examples easy to understand rather than efficient. ( 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 …Fourier analysis. Fourier analysis is named after Joseph Fourier who showed that representing a function by a trigonometric series greatly simplified the study of heat propagation. If you want to find out more, look up fourier synthesis and the fourier transform. ( 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…sform converts a time domain wave form (like a sound wave) into the coefficients of the corresponding Fourier series. A DFT is a digital approximation to a Fourier transform, usually using something like the Cooley-Tuckey Fast Fourier Transform (FFT) for efficiency. The underlying Fourier theorem is something like: Every bounded periodic continuous (needed to avoid Gibbs) function , or wave form, can be written as the sum of its Fourier series. i.e. It is a sum of sines and cosines In otherwords, you take a wave form in the time domain like a sound wave and break it into its components (various frequencies) by the Fourier Transform. The results of the Transform are the coefficients of the Fourier series. The wave form of a voice converted to components (and perhaps a little more) is a voiceprint. ( Full Answer )

# Who is the oldest pitcher in World Series history?

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…roportional to the square of the amount of data being used. So if the amount of data doubles, the amount of effort to calculate the result quadruples. In contrast, the subsequently discovered Fast Fourier Transform requires an amount of effort proportional to the product of the amount of data and the base-two logarithm of the amount of data. Thus, if the amount of data doubles, the amount of effort increases but by less than a quadruple. With each doubling of the data size, the amount of effort increases by a diminishing factor which slowly drops toward but never reaches two. ( Full Answer )

# What is the history of Alabama and Florida football series?

Alabama makes its seventh appearance in the SEC Championship in 2009 against Florida (tenth appearance) in what will be the 36th meeting between the two schools. Florida leads the SEC championship series between the two teams 4-2. Alabama leads the all time series: 21-14

# 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 …expanded then, to the complex plane, and can be applied to non-periodic signals. This gave rise to the Fourier transform, which represents a signal in the frequency-domain.\n.
\nSee links. ( 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/

# Is Twilight the best series in book history?

it depends on your personality if you like action or horror so you won't think it is but if you like romantic books then you will sure say it is. nd most teenagers say it's the best like me ;)

# 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 …equal rights of all is a key factor for social progress. He also is credited by modern scholars for inspiring the foundings of several communist communites in the United States. ( 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 …to filter/manipulate particular frequency components. ( 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…a) / k, for all odd k, 1 to infinity. .
Using a Fourier Transformation, you take take a signal, convert it from time-domain to frequency-domain, apply some filtering or shifting, and convert it back to time-domain. Sometimes, this is easier than building an analog filter, even given that you need a digital signal processor to do it. ( 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…{(a n cos(nx)+b n sin(nx)}... here a o is DC component which gives the amplitude of a signal.. fs of square wave is 4/pi summation(1/n*sin(nw o t) ( 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)… rather than the signal level over time (time 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… the longest period of your original function. A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones. Series: discrete, limited domain Transform: continuous, infinite domain. ( 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.

# Is there going to be a series 3 of horrible histories?

There very well may be but we never now they keep it secret as a suprise I'm afraid! Horrible Histories Series 3 is going to be released on DVD in Spring 2012

# Is there going to be horrible histories series 3?

Yes there is. They are filming it right now and should be out next year.

# 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…se, and you can even make the summation mostly indistinguishable from the aperiodic signal, but the math does not work. ( Full Answer )

# What was the longest game in World Series history?

The longest game in world series history was the New York Giants vs the Philadelphia Athletics. In game 4 of the world series in 1913, the ball game went 31 innings before ending when the New York Giants hit a 3 run home run to end the ball game. The New York Giants ended up winning the world series… 3 to 2( it used to be 5 games in the world series). ( Full Answer )

# 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… frequency of the signal (which coincides with the frequency of the 1st main harmonic). All the harmonics with the number>1 are called higher harmonics, whereas the 1st one is called - the main harmonic. After reminding the mathematical properties of the signal we can maintain, that sometimes harmonics with even or odd numbers are absent at all. There phases are sometimes always equal to 0 and 180 degrees or to 90 and -90 degrees. Fourier series are known to exist in sinus-cosinus form, sinus form, cosinus form, complex form. The choice depends on the problem solved and must be convenient for further analysis. Fourier tranform is invented and adjusted for aperiodic signals with integrated absolute value and satisfaction of Diricle conditions. It's worth saying, that Dirichle conditions is the necessary requirement for Fourier series too. Fourier representation of aperiodic signals is not discrete, but continious and the amplitudes are infinitely small. They play the role of the proportional coefficients. there are links between Fourier series of periodic signal and Fourier transform. These links may be easily found in almost all the books on classical Fourier analysis of signals. For example, see Oppenheim, Djervis and others. ( Full Answer )

# Who is the author of the horrible histories series of books?

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…lephone system itself, where digital filtering is used to minimize bandwidth demands. ( Full Answer )

# Will There be a Horrible Histories Series 4?

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?

In October 1824, Fourier published a scientific paper titled "Remarques generales sur les Temperatures du globe terrestre et des espaces planetaires" in the journal Annales de Chimie et de Physique, Tome XXVII (pp.136-167), in which he presented his results from a mathematical analysis, that climate…-change experts today (the ones who actually are experts) generally regard as the start of climate-change science. ( Full Answer )

# What is the history of Need For Speed series?

the need for speed series is an electronic art franchise that have produced car racing games since the 1990s with initial games focusing on more acade type action packed racing like the need for speed 1 and need for speed: hot pursuit. Need for speed:underground was a success introducing an exciting… night street racing with highly visually costumizable cars. The 2005 NFS mostwanted was also a favourite amongs the fan. But sales dropped in the subsequent games until 2009 Nfs: shift which saw the the franchise return to the more simulation type racing they introduce earlier in Nfs prostreet. It also return the corkpit view as in the much earlier Nfs Porshe unleashed. Other remarkable titles like the criterion develop 'NFS: hot pursuit' in 2010 and 2011 Shift: Unleashed. Which marks the franchise recent line of simulation professional racing game titles. The latest and largest in game size is the Need for Speed : the Run. ( Full Answer )

# 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 …/ Capacitors / Inductors together with some Non Linear Devices / Active Amplifiers etc. in different combinations to get the desired results , on analog signals in particular range of Frequency & Amplitudes. It is very difficult to Do such operations on a wide range signals using a particular combination od circuits. Another alternative is to Digitise the Analog Signal , so that Any Suitable Mathematical Operations can be done easily & then reconvert the Processed Digital Signal back to Analog form when required. An important fact to note is that Storage of the Purely Analog Signals & Retrival is an Expensive & Lossy affair ( signal stored may degrade / get corrupted ), as is evident in Magnetic Audio / Video Tapes , Phonographic Records etc.which were the Most Popular Methods of Analog Signal Storage. So a Digitised Format would be vastly more convenient from today's technological point of view. ( 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…ting for electrical engineering because a signal canbe a function of time and it can also be a function of frequency.These two representations of the same signal form aFourier-Transform pair. So the spectrum is the FT of the waveform,while the waveform is reverse-FT of the spectrum. Fourier series are also good because they are the simplest exampleof the whole new subject of orthogonal polynomials, and these arealso important in engineering because they are used to findsolutions of the differential equations that are thrown up byphysical systems. So, while a violin string can be analysed by a Fourier series whichexplains the harmonics that give a violin its distinctive sound,something more complex like a drum-skin can also be analysed, butthe answer comes out in terms of another type of orthogonalfunction, the Bessel functions, instead of circular functions(sines and cosines). This explains why you get a note from a drumbut it's less well defined, because the upper modes are notharmonically related to the fundamental. ( Full Answer )

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

The word sine, not sinx is the trigonometric function of an angle. The answer to the math question what is the four series for x sine from -pi to pi, the answer is 24.3621.

# What is the history of the 'Children of the Corn' series of films?

The 'Children of the Corn' series of films was based on the short story by Stephen King. 8 film episodes were released between 1984 and 2011, and can be purchased on video.

# What does the Fourier time series analysis help with in signal processing?

It is difficult to describe how Fourier time series analysis helps with signal processing without going into deep detail. Basically, it helps to manipulate the data to be understood in a simpler way. For the complete detailed explanation one can view Wikipedia "Fourier Analysis".

# What properties or conditions should fx satisfy such that fx equals its fourier series?

The properties and conditions of FX to satisfy such that the fx equals its fourier seasons, should be of the fans, and the ones that actually watch the awseome series that are on FX. Lots of people are huge fans of FX and really get destroyed when there is no satisfaction of the fourier seasons.

# 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 …then back converting to timedomain. The sky is the limit in terms of what you can do withfourier series analysis. ( Full Answer )

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

A Fourier series is a set of harmonics at frequencies f, 2f, 3fetc. that represents a repetitive function of time that has aperiod of 1/f. A Fourier transform is a continuous linear function. The spectrumof a signal is the Fourier transform of its waveform. The waveformand spectrum are a Fourier tra…nsform pair. ( Full Answer )

# 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".