Determine the bn of the Fourier Series of Determine the b, of the Fourier Series of:-15; -3

Introduction: Suppose, a one cycle a continuous periodic function is defined on the interval -P,P.…

Answered: Determine the b, of the Fourier Series…

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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In the Fourier Series an and bn (for any n) are found by multiplying the signal by the nth harmonic (i.e. cos nx or sin nx), and then integrating. This works because multiplying any sinusoid (signal) by a sine or cosine results in a curve with an integral of A if the harmonic (n) is NOT present in the original signal. This process (multiplying the signal by a sinusoid of known frequency and integrating) is called A/ Reminder: Fourier Series: f(x)= ao + Σ(ancosx + b sinx), for all n
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Please solve this question as soon as possible in fourier series
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 = 0
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Determine the b, of the Fourier Series of: f(t) = { -15; -3