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- In the Fourier Series an and bn (for any n) are found by multiplying the signal by the nth harmonic (i.e. cos nx or sin nx), and then integrating. This works because multiplying any sinusoid (signal) by a sine or cosine results in a curve with an integral of A if the harmonic (n) is NOT present in the original signal. This process (multiplying the signal by a sinusoid of known frequency and integrating) is called A/ Reminder: Fourier Series: f(x)= ao + Σ(ancosx + b sinx), for all n3. Show that the Fourier series of the function g(x) = |x|| on the interval [-7,7] is 4 g(r) =5 - 1 cos(2n – 1)x %3D 2 (2n – 1)2 - n=1Find at least three nonzero terms (including ao and at least two cosine terms and two sine terms if they are not all zero) of the Fourier series for the given function, and sketch at least three periods of the function. Which of the following is the Fourier series for the given function? f(x) = 2 O A. f(x) = O B. f(x)= π 4 O D. f(x)= π 4 NI 2 π O c. f(x) = 2 π 2 π + π 4 - π 4 π COS X- COS X- - sin x + COS X- - 4 9μ 4 9μ 4 9₁ 4 - cos 3x... - - sin x- π 4 9μ cos 3x - ... sin 3x + . cos 3x - ... + 4 - sin x + π 4 9μ 4 9μ sin 3x - ... sin 3x + ... f(x) = -X ≤x<0 X 0≤xFind the Fourier series representation of the even extension of the function f(x) = = mx + b dm + b Then, find the value of an if m= 9.7, b = 6.93, d = 5, and n = 11. Round off the final answer to five decimal places. if 0 < xshow that the fourier series of the function ?(?) = |?| ?? [−?, ?] is :2a. Expand the function f(0)=0² in a Fourier series in the range –A<0Find the Fourier series for the given function. f(x) = 9 2⁰⁰ 9 2 πm=12m - f(x) = 9 - - Σ 100 9 Im=1M - 1 f(x) = 20⁰ 9 Σ πm=12m - 1 f(x): = - 200 9 Σ πm=12m 2 9 9 °ƒ(x) = ²/1 + ² £; Σ 2 πm=12m - 9|N9|N 2 -sin 1 -sin f(x) = {% (2m 1)лx L (m1)лx L (2m — 1)лx) L (2m — 1)лx - L (2m − 1)лx) L 9, L≤ x < 0, 0 ≤ x < L; ¡cos((2m. -sin 1 -7cos (12m- -COS 1 f(x + 2L) = f(x)Find the Fourier Series for the following funcioin fx) on the interval -1L X E l, Please Show all steps. fxo=Dx+Sin TXRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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