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Suppose that f(t) is periodic with period [-, ) and has the following complex Fourier coefficients: co= 5, c₁=-1-2i, c₂=-3-3i, c3 = 2-3i, ... ... (A) Compute the following complex Fourier coefficients. C_3== C_2= (B) Compute the real Fourier coefficients. (Remember that ei kt = cos(kt) + i sin(kt).) ao a₂=₁, az = a₁ = b₁ = (C) Compute the complex Fourier coefficients of the following. (i) The derivative f'(t). a=0 8 0₂ C3== = (ii) The shifted function f(t +) C1 = (iii) The function f(3t). C3= C2 =

Suppose that f(t) is periodic with period [-, ) and has the following complex Fourier coefficients: co= 5, c₁=-1-2i, c₂=-3-3i, c3 = 2-3i, ... ... (A) Compute the following complex Fourier coefficients. C_3== C_2= (B) Compute the real Fourier coefficients. (Remember that ei kt = cos(kt) + i sin(kt).) ao a₂=₁, az = a₁ = b₁ = (C) Compute the complex Fourier coefficients of the following. (i) The derivative f'(t). a=0 8 0₂ C3== = (ii) The shifted function f(t +) C1 = (iii) The function f(3t). C3= C2 =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that f(t) is periodic with period [-T, T) and has the following complex Fourier coefficients: ... Co=5, C₁=-1-2i, c₂=-3-3i, c3=2-3i, ... (A) Compute the following complex Fourier coefficients. C-3 = C_2= C-1 = (B) Compute the real Fourier coefficients. (Remember that ei kt = ao = 0, 1, a₂ = a3 = b₁ = ₁ b₂ = ₁ b₂ = b3 = (C) Compute the complex Fourier coefficients of the following. (i) The derivative f'(t). C₁=0 C1 = CO Co= a1 = C₂ = (ii) The shifted function f(t + 7) C1 = Co= C2 C₂ = C3 = (iii) The function f(3t). C1 = C3 = C2 = C3 = cos(kt) + i sin(kt).)
Transcribed Image Text:Suppose that f(t) is periodic with period [-T, T) and has the following complex Fourier coefficients: ... Co=5, C₁=-1-2i, c₂=-3-3i, c3=2-3i, ... (A) Compute the following complex Fourier coefficients. C-3 = C_2= C-1 = (B) Compute the real Fourier coefficients. (Remember that ei kt = ao = 0, 1, a₂ = a3 = b₁ = ₁ b₂ = ₁ b₂ = b3 = (C) Compute the complex Fourier coefficients of the following. (i) The derivative f'(t). C₁=0 C1 = CO Co= a1 = C₂ = (ii) The shifted function f(t + 7) C1 = Co= C2 C₂ = C3 = (iii) The function f(3t). C1 = C3 = C2 = C3 = cos(kt) + i sin(kt).)
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