Using a continuous wavelet transform, the wavelet Gibbs phenomenon never exceeds the Fourier Gibbs phenomenon. In practice, the difficulties associated with the Gibbs phenomenon can be ameliorated by using a smoother method of Fourier series summation, such as Fejér summation or Riesz summation, or by using sigma-approximation.
See Convergence of Fourier series § Absolute convergence. This expression allows you to create a looping wiggle by cleverly animating between 2 different wiggle expressions. Dan Ebbert has a sweet little write up regarding this, and it essentially boils down that when you use the wiggle expression, it returns an array of values.
However, it doesnt loop easily by default. By the same token, it is impossible for a discontinuous function to have absolutely convergent Fourier coefficients, since the function would thus be the uniform limit of continuous functions and therefore be continuous, a contradiction. The Wiggle Expression is one of the most common and useful expressions for adding randomness and variation to properties in After Effects. This only provides a partial explanation of the Gibbs phenomenon, since Fourier series with absolutely convergent Fourier coefficients would be uniformly convergent by the Weierstrass M-test and would thus be unable to exhibit the above oscillatory behavior. In mathematics, the Gibbs phenomenon is the oscillatory behavior of the Fourier series of a piecewise continuously differentiable periodic function around a jump discontinuity.
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