Gibbs Phenomena
By considering the periodic sawtooth function, we show that the partial sums of its Fourier series have a first positive maximum value at pi/(n+1). The value of the partial sums at these maximal values converge as n tends to infinity to the sinc function integrated from zero to pi. Numerically, this is 9% more that the value of the jump at the origin. This is known as Gibbs Phenomena, and it is valid for functions which have a jump discontinuity in more generality. The partial sums of the Fourier series overcorrect for the jump discontinuity.
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