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The components of the Fourier series are given by
The Fourier series is therefore given by
The example of periodic square wave can be also used to illustrate Fourier approximation.
Consider a square wave of length 2L over the range [0, 2L]. The functional form of the
configuration
where H(x) is the Heaviside step function. Since
, the function is odd,
so
, and
The Fourier series is therefore
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