Suppose that f(t) is periodic with period [-x, x) and has the following complex Fourier coefficients: C1 = -3+ 4i, 2 =-1- 2i, C3 = 2, (A) Compute the following complex Fourier coefficients. (B) Compute the real Fourier coefficients. (Remember that e t cos(k t) + i sin(kt).) ao = , a = by , by= %3D (C) Compute the complex Fourier coefficients of the following. (1) The derivative f'(t). (ii) The shifted function f(t + (ii) The function f(3t). Co

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Suppose that f(t) is periodic with period [-n, 7) and has the following complex Fourier coefficients:
2i,
2,
-4,
C1
-3+ 4i, C2 = -1
C3
(A) Compute the following complex Fourier coefficients,
C_3
C_2
(B) Compute the real Fourier coefficients, (Remember that et kt
cos(kt) + i sin(kt).)
ao =
, a1 =
, a2 =
, az =
b1
b2
63 =
(C) Compute the complex Fourier coefficients of the following.
(i) The derivative f' (t).
Co =
C1
C2 =
C3 =
(ii) The shifted function f(t +
Co =
C =
C2 =
C3 =
(iii) The function f(3t)
Co =
C4 =
C2 =
C3 =
Transcribed Image Text:Suppose that f(t) is periodic with period [-n, 7) and has the following complex Fourier coefficients: 2i, 2, -4, C1 -3+ 4i, C2 = -1 C3 (A) Compute the following complex Fourier coefficients, C_3 C_2 (B) Compute the real Fourier coefficients, (Remember that et kt cos(kt) + i sin(kt).) ao = , a1 = , a2 = , az = b1 b2 63 = (C) Compute the complex Fourier coefficients of the following. (i) The derivative f' (t). Co = C1 C2 = C3 = (ii) The shifted function f(t + Co = C = C2 = C3 = (iii) The function f(3t) Co = C4 = C2 = C3 =
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