Calculating Fourier Series for an Odd Function

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SUMMARY

The discussion focuses on calculating the Fourier Series for a piecewise function defined as f(t) = 5 for intervals [0, 0.2s] and [0.6s, 0.8s], and f(t) = 0 for [0.2s, 0.6s]. The key equations for an odd function are provided, specifically a0 = 2/p * integral(from -p/2 to p/2) of f(t) dt and bn = 4/p * integral(from 0 to p/2) of f(t)*sin(2*pi*n*t/p) dt. The challenge arises from the function being "off" for longer periods, necessitating the use of general formulas for both a and b coefficients, as the function does not exhibit odd or even symmetry.

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Homework Statement



f(t) is given as:

from 0 to 0.2s, f(t) = 5
from 0.2s to 0.6s, f(t) = 0
from 0.6s to 0.8s, f(t) = 5,
etc

Homework Equations


for an odd function

a0 = 2/p * integral(from -p/2 to p/2) of f(t) dt

bn = 4/p * integral(from 0 to p/2) of f(t)*sin(2*pi*n*t/p) dt

The Attempt at a Solution



The problem is that since the function is "off" for a longer period than it is "on"; I'm not sure how to incorporate that into the Fourier Series, especially the bn term
 
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The function f(t) is neither odd nor even, so you have to use the general formulas for the coefficients, both the a's and b's.
 

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