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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![Q7. Find the Fourier series of the signal f(t), with period 27, given on the interval [-, π]
by
f(t):
=
-1,
1,
0,
for-/2 < t < 0,
for 0 < t < π/2,
otherwise.](https://content.bartleby.com/qna-images/question/e781e991-850f-4092-9b36-3deffb65313c/9e42462c-f32c-4a20-b769-b53ad69e3f75/yma58nk_thumbnail.png)
Transcribed Image Text:Q7. Find the Fourier series of the signal f(t), with period 27, given on the interval [-, π]
by
f(t):
=
-1,
1,
0,
for-/2 < t < 0,
for 0 < t < π/2,
otherwise.
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- Suppose 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 = 0arrow_forward2 Denote the Fourier series of f(z) = { -x, 0arrow_forward
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