Finding Fourier Coefficients-Matlab
$15-20 USD
Teslim sırasında ödenir
The program finds N terms of Fourier coefficients for any function F(x). The Matlab program finds:
F(x) =Fourier Series===> A_0 + Sum_k[ A_k cos(kx) + B_k sin(kx) ]
-A_0
-the cosine kth coefficient
-the sine kth coefficient
For a periodic function *?*(*x*) that is integrable on [−*π*, *π*], the numbers
: ![a_n = \frac{1}{\pi}\int_{-\pi}^\pi f(x) \cos(nx)\, dx, \quad n \ge 0][1]
and
: ![b_n = \frac{1}{\pi}\int_{-\pi}^\pi f(x) \sin(nx)\, dx, \quad n \ge 1][2]
are called the Fourier coefficients of *?*. One introduces the *partial sums of the Fourier series* for *?*, often denoted by
: ![(S_N f)(x) = \frac{a_0}{2} + \sum_{n=1}^N \, [a_n \cos(nx) + b_n \sin(nx)], \quad N \ge 0.][3]
The partial sums for *?* are [trigonometric polynomials][4]. One expects that the functions *S**N* *?* approximate the function *?*, and that the approximation improves as *N* tends to infinity. The [infinite sum][5]
: ![\frac{a_0}{2} + \sum_{n=1}^\infty \, [a_n \cos(nx) + b_n \sin(nx)]][6]
is called the **Fourier series** of *?*.
<[url removed, login to view]>
Proje NO: #3702358