13.4 CONDITIONS FOR EXISTENCE OF FOURIER SERIES
The exponential and trigonometric Fourier series exists for all v(t) which satisfy a set of conditions known as Dirichlet's conditions (see side-box).
There are functions that violate one or more of Dirichlet's conditions. But they do not come up in Electrical Circuits. Hence, we can safely assert that all waveforms we encounter in physical circuits will satisfy these conditions.
If v(t) satisfies all the Dirichlet's conditions, its Fourier series is guaranteed to exist and converge to the function value except at the points of discontinuity. At the points of discontinuity, the Fourier series will converge to the average value – i.e., to half the sum of value of v(t) at the left and right of the ...
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