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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.
Is the infinite sum of continuous function continuous?
An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
What are the limitation of fourier series?
what are the limitations of forier series over fourier transform
Can a discontinuous function can be developed in the Fourier series?
Yes. For example: A square wave has a Fourier series.
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.
Is tan x has fourier expansion?
y=tanx cannot be expressed as a Fourier series, since it has infinite number of infinite discontinuity. Dirichlet’s condition or the sufficient condition for a function f(x) to be expressed as a Fourier series. - f(x) is single valued, finite and periodic. - f(x) has a finite number of finite discontinuities. f(x) has a finite number of maxima and minima. - f(x) has no infinite discontinuity.
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.
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 has the author Leonida Tonelli written?
Leonida Tonelli has written: 'Serie trigonometriche' -- subject(s): Fourier series, Infinite Series
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 periodicsignal. 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.
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 are Joseph Fourier's works?
Fourier series and the Fourier transform
Is the infinite sum of continuous function continuous?
An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
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.
