Experiment 4:Gibbs Phenomenon Introduction In Fourier Synthesis,adding successive harmonics brings the waveform,closer and closer to the desired shape.However,you'll find that the synthesizer has most difficulty in producing sharp discontinuities in a waveform,such as the instantaneous drop or rise at the corners of a square wave.This is true in Fourier Synthesis in general,and is known as Gibbs Phenomenon.At these discontinuities in the waveform there is generally an overshoot as harmonics are added,as of the harmonics are trying to make the corner,but always go a bit too far before they can get turned around.Gibbs demonstrated that the amount of overshoot does not depend on the number of harmonics used,but the width of each overshoot peak becomes narrower as the number increases. With an infinite number of harmonics,of course,the sum of the harmonics exactly reproduces the waveform.Unfortunately,that's a little tough to demonstrate. Procedure Repeat the procedure of Experiment 3 for building a square wave or other waveform. As each harmonic is added,measure the amount of overshoot and the width of the overshoot peaks.5 Experiment 4: Gibbs Phenomenon Introduction In Fourier Synthesis, adding successive harmonics brings the waveform, closer and closer to the desired shape. However, you'll find that the synthesizer has most difficulty in producing sharp discontinuities in a waveform, such as the instantaneous drop or rise at the corners of a square wave. This is true in Fourier Synthesis in general, and is known as Gibbs Phenomenon. At these discontinuities in the waveform there is generally an overshoot as harmonics are added, as of the harmonics are trying to make the corner, but always go a bit too far before they can get turned around. Gibbs demonstrated that the amount of overshoot does not depend on the number of harmonics used, but the width of each overshoot peak becomes narrower as the number increases. With an infinite number of harmonics, of course, the sum of the harmonics exactly reproduces the waveform. Unfortunately, that's a little tough to demonstrate. Procedure Repeat the procedure of Experiment 3 for building a square wave or other waveform. As each harmonic is added, measure the amount of overshoot and the width of the overshoot peaks