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My formula booklet in signals analysis states that a condition for the Fourier series of a periodic function $x(t)$ to exist is that one period of $x(t)$ contains a finite number of maxima and minima.

Is this true, and does it mean that I can't find the Fourier series of a square wave? (Because I just did.)

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    The series will converge to the right value at all **continuous points**. At discontinuous ones, it converges to the Cauchy principal value (average of the right- and left- sided limits). You can check that your Fourier series gives exactly this type of behaviour.2017-10-08

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