Finding Fourier Coefficients-Matlab

İptal Edildi İlan edilme: Nov 17, 2011 Teslim sırasında ödenir
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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 *?*.

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