- #1
therimalaya
- 7
- 0
May be simple, but I'm getting problem with doing Fourier series expansion of Sin(x) for -pi[tex]\leq[/tex]x[tex]\leq[/tex]pi
CompuChip said:What does the formula for the Fourier expansion of a general function f(x) look like?
Defennder said:Isn't it supposed to be 1/pi for both a_n and b_n and 1/2pi for a_0? And in the formulae for a_n, b_n, these are supposed to be definite integrals not indefinite ones.
CompuChip said:Anyway, for the sine you can either calculate all these
----------------
HallsOfIvy, you may be right, didn't notice that. Asked the mods to look into it and maybe split the thread.
A Fourier series expansion of Sin(x) is a mathematical representation of a periodic function (in this case, Sin(x)) as a sum of sinusoidal functions with different frequencies and amplitudes. It is named after the mathematician Joseph Fourier who first introduced the concept in the 19th century.
A Fourier series expansion of Sin(x) is calculated using the Fourier series formula, which involves integrating the function over one period and multiplying it by a series of trigonometric functions (e.g. sin(nx), cos(nx)) with varying coefficients. This process results in an infinite sum, which can be approximated by truncating the series to a finite number of terms.
A Fourier series expansion of Sin(x) is significant because it allows us to represent a periodic function using a simpler and more compact form. It also has many applications in fields such as signal processing, differential equations, and quantum mechanics.
Yes, a Fourier series expansion of Sin(x) can be used to approximate any periodic function with a finite number of terms. However, the accuracy of the approximation depends on the smoothness of the function and the number of terms used in the series.
Yes, there are many real-world applications of Fourier series expansion of Sin(x). Some examples include audio signal processing, image compression, and power analysis in electrical engineering. It is also used in areas such as weather forecasting, medical imaging, and pattern recognition.