Find the Fourier series of the functions Ekez max(1 – |x – k|, 0) - and Ekez max(1 – |r – k/2|,0). ΣκεZ Inax(
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- 3.Find the Fourier series of the function wmww w f(x)= f(x)=x OsxST f(x)=t TISXS2TObtain complex Fourier series of f(t) = t|t| if |t| < πt Graph f(t)Find the Fourier series to represent a function of a.) f(x) = x + 1, - 2< x< 0, = 1, 0Q) for the following function: (X + 4) - 4 sx<-2 F(x) -X - 2sx< 2 (х - 4) 2sx < 4 1. Draw the function and is the function even or odd or neither? 2. Determine the Fourier coefficients, then write at least three terms of the Fourier series expansionSuppose that f(t) is periodic with period -T, 7) and has the following real Fourier coefficients: a2 = 3, аз — 3, b2 = -3, b3 = 0, ao 4, a1 = 1, b, = 2, (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) = 2+cost+2sint+3cos2t-3sin2t+3cos3t+0+. (B) Give the real Fourier coefficients for the following functions: (i) The derivative f'(t) ao = , a1 = -1 , az = -6 , az = -9 b, = 2 , b2 = -6 bz = (ii) The function f(t) – 2 ao = , a1 = , az = 3 , аз — 3 b1 = 2 , b2 = -3 bz = (iii) The antiderivative of (f(t) 2) (with C 0) ao = , a1 , a2 = 3/2 , аз 1 b1 =-2 b2 = 3/2 b3 = (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) ao = 2 , a1 = 1 , a2 = 6 , аз — 3 b, = 2 b2 = -3 b3 = 3 (iv) The function f(2t) an =2 , a1 , a2 3 , a3 3 b, = 2 , b2 = -3 b3 = 0Find the trigonometric Fourier series for the square 2n-periodic wave defined on the interval [-11,1]: f(x) = {0, if-SX<0 f(x) = {1, if 06. Find the Fourier series of the function (-Ħ < x < 0) 0, f (x, y) = %3| sin r, (0 < r < n). Use this series to conclude that =1-2 - 2In = 1× (-1)" 4n2-12. Find the Fourier series for the function f(r) =. 27 27 ,f (z + 47) = f(r).* (30) 13 Find the Fourier transform of (x) = LIOBLEON 3x ifbxK1 O if | x | > 1 ={₁ IISEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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