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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.
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Discontinuous function in fourier series?
yes a discontinuous function can be developed in a fourier series
Fourier series of sine wave?
The fourier series of a sine wave is 100% fundamental, 0% any harmonics.
What is harmonic as applied to fourier series?
When we do a Fourier transformation of a function we get the primary term which is the fundamental frequency and amplitude of the Fourier series. All the other terms, with higher frequencies and lower amplitudes, are the harmonics.
In Fourier transformation and Fourier series which one follows periodic nature?
The 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. The 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. See links.
What is relation between laplace transform and fourier transform?
The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes ofvibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations.
What are Joseph Fourier's works?
Fourier series and the Fourier transform
What are the limitation of fourier series?
what are the limitations of forier series over fourier transform
Discontinuous function in fourier series?
yes a discontinuous function can be developed in a fourier series
How do you find the inverse Fourier transform from Fourier series coefficients?
no
Can a discontinuous function can be developed in the Fourier series?
Yes. For example: A square wave has a Fourier series.
What is physical significance of Fourier series?
Fourier series is series which help us to solve certain physical equations effectively
What is the difference between fourier series and discrete fourier transform?
Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
Fourier series of sine wave?
The fourier series of a sine wave is 100% fundamental, 0% any harmonics.
Why was Joseph Fourier famous?
Joseph Fourier was the French mathematician and physicist after whom Fourier Series, Fourier's Law, and the Fourier Transform were named. He is commonly credited with discovering the greenhouse effect.
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.
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.
What is harmonic as applied to fourier series?
When we do a Fourier transformation of a function we get the primary term which is the fundamental frequency and amplitude of the Fourier series. All the other terms, with higher frequencies and lower amplitudes, are the harmonics.
