The Fourier series of waveforms with discontinuties experiences an overshoot near the discontinuity known as the "Gibbs phenomenon". There is quite a bit of literature showing that the overshoot for a rectangle function is ~ 1.089. What about other functions such as (1-x) or a decaying exponential for x positive? Is there any reason to expect the overshoot ratio to be identical to the rectangle function? I do know for a fact that the behavior of the overshoot is different for the triangle function (1-x) than for the rectangle function. For low harmonics there is an undershoot for the triangle function case, but this is not the case for the rectangle function. The overshoot occurs for the triangle function after a sufficient number of terms are included in the Fourier series. The same is true for the decaying exponential. This is illustrated in my worksheet linked below.
Does anyone know of MAPLE code that computes the theoretical overshoot if there is an infinite number of terms in the series for different waveforms or functions?