Electric Circuit Analysis

Waveform Symmetry and Fourier Series Coefficients 9.11

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 discontinuity.

This implies that, for a v(t) that satisfies all the four conditions, the partial sum of its Fourier

series tends to approach the value of v(t) as the number of series terms included in the partial sum

approaches infinity.

lim ( ) ( )

N

n

jn t