Suppose that f(t) is periodic with period [-T, 7) and has the following complex Fourier coefficients:-4,C1—3+ 41, С2 —D —1- 21,C32.(A) Compute the following complex Fourier coefficients.C_3 =2C_2 =-1+2iC_1 =(B) Compute the real Fourier coefficients. (Remember that ei ktcos(kt) + i sin(kt).)ao =a1 =-6, a2 =-2, az =4b, =b2 =b3 =(C) Compute the complex Fourier coefficients of the following.(i) The derivative f' (t).Co =C1 =-4-31C2 =C3 =(ii) The shifted function f(t +Co =C =C2 =C3 =(iii) The function f(3t).Co =C =C2 =C3 =

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Suppose that f(t) is periodic with period -, x) and has the following complex Fourier coefficients: Co = -4, C= -3+ 41, --1 - 21, (A) Compute the following complex Fourier coefficients. e=-1+21 (B) Compute the real Fourier coefficients. (Remember that e kt = cos(k t) +i sin(kt)) -6 -2 az 4 b = , by = , by=0 (C) Compute the complex Fourier coetficients of the following. (1) The derivative f' (t). C--4-31 (1) The shifted function f(t + () The function f(3t). Co =

Suppose that f(t) is periodic with period -, x) and has the following complex Fourier coefficients: Co = -4, C= -3+ 41, --1 - 21, (A) Compute the following complex Fourier coefficients. e=-1+21 (B) Compute the real Fourier coefficients. (Remember that e kt = cos(k t) +i sin(kt)) -6 -2 az 4 b = , by = , by=0 (C) Compute the complex Fourier coetficients of the following. (1) The derivative f' (t). C--4-31 (1) The shifted function f(t + () The function f(3t). Co =

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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Question

Suppose that f(t) is periodic with period [-T, 7) and has the following complex Fourier coefficients:
-4,
C1
—3+ 41, С2 —D —1- 21,
C3
2.
(A) Compute the following complex Fourier coefficients.
C_3 =
2
C_2 =-1+2i
C_1 =
(B) Compute the real Fourier coefficients. (Remember that ei kt
cos(kt) + i sin(kt).)
ao =
a1 =
-6
, a2 =
-2
, az =
4
b, =
b2 =
b3 =
(C) Compute the complex Fourier coefficients of the following.
(i) The derivative f' (t).
Co =
C1 =
-4-31
C2 =
C3 =
(ii) The shifted function f(t +
Co =
C =
C2 =
C3 =
(iii) The function f(3t).
Co =
C =
C2 =
C3 =

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