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- function ob tain the fourier series for the Y-TT Per iodic o'dd fM x(ホーm) if ne [e,T] 1 ( Ttl) if HE [-T,0]1) Derive the Fourier transform of functions Description Delta function in x Delta function in k Exponential in Exponential in k Gaussian Function 8(x) 1 Transform 1 2πδ(k) (a > 0) 2a a²+k² 2πe-alk (a>0) √2πe-k²/2I need help with question and show your work need as soon as possbile
- A periodic function, f(x) with period 4x is defined as - 2n sx<-1 - nSX<0 2n, %3D f(x) Osx<* 2n, Sketch the graph of f(x) on the interval [-5x, 57). Determine if f(x) is an even, odd or neither even nor odd function. a) b) Find the Fourier series of f(x).I need help with question show all your work pleaseMATHEMATICAL METHODS :Please quickly , only choose the correct answer
- Please solve it ASAP, thank you!Exercises 3 Let f(x) be a function of period 27 such that f(x) = x in the range - T2. Consider the function f(x) = 1 x on the interval [0, 1]. a) In two separate graphs, sketch i) the odd extension fodd on the interval [-1,1], ii) the Fourier series associated with fodd on the interval [-3,3]. b) Carefully state Fourier's theorem, including the definition of the Fourier series and the Fourier coefficients. c) Compute the Fourier coefficients of fodd and write down the Fourier series. Give full justification for your answer. d) By evaluating the Fourier series for an appropriate value of x, show that 1 2 2 2 2 3π 5TT 7π = 2|7 + +Determine the Fourier Series of f(x) = x², over the interval - < x < and has period 2 ! f(x) = 3r [c cos x + cos 3x + cos 5x + .] sina+sin 2x + sin 3x +... 2 1 1 f(x) sin x + sin 3x + sin 5x + 1 π 3 5 1 1 -{sin z + sin 2x + sin 3x + x ...} 2 2 3 $ 1 f(2)=-4 [cos 2-2008 22 +00832 - 008 42 + cos cos cos 4x 4] 3 4² = # f(x) 12 = Todule code: CAPE200001 [a, -1Please do b and please do not type the answerRecommended textbooks for youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage Learning
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