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# What is the history of fourier series?

# 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.

# 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 correspo…nding 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.

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

yes it can, if you know how to use or have mathematica have a look at this demo http://demonstrations.wolfram.com/ApproximationOfDiscontinuousFunctionsByFouri…erSeries/

# 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.

# 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.

# Fourier series of sine wave?

The fourier series of a sine wave is 100% fundamental, 0% any harmonics.

# 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.

# 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 allo…ws 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.

# 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.

# 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.

# What are the limitation of fourier series?

what are the limitations of forier series over fourier transform

Answered

# 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 the…n converted back to time domain; your cell phone or its headset, if it has advanced noise cancellation technology; and the telephone system itself, where digital filtering is used to minimize bandwidth demands.

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In Calculus

# 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...mixi…ng 2 signals produces a diff 1..like tat wen sine and cosine is mixed a diff required signal is produced.. ao/2+summation{(ancos(nx)+bnsin(nx)}... here ao is DC component which gives the amplitude of a signal.. fs of square wave is 4/pi summation(1/n*sin(nwot)

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# 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 repres…ent a periodic signal. Since an aperiodic signal is not periodic, the fourier series does not apply to it. You can come close, and you can even make the summation mostly indistinguishable from the aperiodic signal, but the math does not work.

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In Technology

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

In electrical engineering, the Fourier series is used to analyse signal waveforms to find their frequency contest. This is needed to design communication systems that will… deliver the signal to the receiver in good shape. If you go on to study the next step, the Fourier Transform, that is really interesting for electrical engineering because a signal can be a function of time and it can also be a function of frequency. These two representations of the same signal form a Fourier-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 example of the whole new subject of orthogonal polynomials, and these are also important in engineering because they are used to find solutions of the differential equations that are thrown up by physical systems. So, while a violin string can be analysed by a Fourier series which explains the harmonics that give a violin its distinctive sound, something more complex like a drum-skin can also be analysed, but the answer comes out in terms of another type of orthogonal function, the Bessel functions, instead of circular functions (sines and cosines). This explains why you get a note from a drum but it's less well defined, because the upper modes are not harmonically related to the fundamental.

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In Educators

# 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, 3f etc. that represents a repetitive function of time that has a period of 1/f. A Fourier transform is a… continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.