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- Which of the following is NOT a valid expression for a Fourier coefficient of function f(t) with period 4m? Ⓒao=ff(t)dt be=ff(t) sin(6t)dtas= f(t) cos(3t)dt ao=/f f(t)dt Which of the following are valid for Fourier coefficients of 1 t ≤ 4T f(t)= = {1 0 4 < t < 8T with period 16. [Tick all that apply - points will be deducted for wrong answers.] 1 Ⓒao = 16-80 fdt = □bk=0ak = cos(kt)dt 14 -4T ak cos()dt 8m ak = 8x 8K -8T cos(k)dt Which of the following expressions is NOT equal to zero? ○ 813 Of sin(3x) sin(a)da of sin(3x) cos(x) dx 12m Of* sin(2x) dx of cos(3x) cos(3x)daa)Suppose that f(t) is periodic with period [-n, n) and has the following complex Fourier coefficients: Co = -3, 1 = -3+3i, C2 = 3, C3 = -4 + 2i, ... ... (A) Compute the following complex Fourier coefficients. C3 = (B) Compute the real Fourier coefficients. (Remember that et kt = cos(kt) + i sin(kt).) %3| ao = > a2 = > az = bi bz = %3D (C) Compute the complex Fourier coefficients of the following. (1) The derivative f (t). Co (ii) The shifted function f(t +) Co C2 Ca= (iii) The function f(3t). Co C1 = %3D
- please label the question and answer clearly. also please answer part D and E. thank you!!!Letr (1) = (sin (1), cos (1), 4 sin (1) + 5 cos (2r)). Find the projection of r(t) onto the xz-plane for -1 ≤ x ≤ 1. (Use symbolic notation and fractions where needed.) z (x) =a) Exeand in fourier series the perio dic Lunction X+2, -2(b) Determine the Z-transforms of the following expressions (ii) (cos 0 + i sin 0)"9(3) Compute an approximation of f(x) = tanx by computing the coefficients Co, C₁, C2, C3 (a = 0). Then graph y = tan x and the obtained cubic polynomial in the same coordinate system. As you zoom on the origin (0, 0) do these two graphs get closer?Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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