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Q.2: Find the Fourier coefficients of the periodic function f(x) its formula; Take n= 1 to 4: f(x) = π - x if - π

Q.2: Find the Fourier coefficients of the periodic function f(x) its formula; Take n= 1 to 4: f(x) = π - x if - π

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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Step 1: Fourier series

f(x) is defined in (−π , π).

f(x) is periodic with period 2π.

f(x) is continuous in (−π,π).

f(x) has jump discontinuty at −π and π

The Fourier series of f(x) defined as

f(x)≈a02+∑n=1∞[ancos⁡(nx)+bnsin⁡(nx)]

Where

an=1π∫−ππf(x)cos⁡(nx)dx 

For n=0,1,2,⋯

bn=1π∫−ππf(x)sin⁡(nx)dx

For n=1,2,⋯

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