# 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.

# 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.

# 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 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 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.

# Discontinuous function in fourier series?

yes a discontinuous function can be developed in a fourier series

# Differences between full range Fourier series and a Half range Fourier series?

half range--- 0 to x full range--- -x to x

# 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 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.. 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)

# What is the physical significance of fourier series?

Fourier series is series which help us to solve certain physical equations effectively

# 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.

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# Fourier series of sine wave?

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

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# What are the limitation of fourier series?

what are the limitations of forier series over fourier transform

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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.

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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 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.

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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.