I can suggest alternative signal processing techniques that are less prone to the Gibbs phenomenon. One approach is to use wavelets, which are mathematical functions that can be used to decompose signals into different frequency bands. By using wavelets, one can reconstruct signals that have discontinuities without the ringing artifacts associated with Fourier series. Another approach is to use high-order finite element methods, which can accurately represent complex geometries and discontinuities in signals.

In addition, one can also use non-linear signal processing techniques, such as neural networks, to reconstruct signals with discontinuities. These methods can learn the underlying structures and patterns in the signal and are less prone to the Gibbs phenomenon. Overall, there are various alternative signal processing techniques that can be used to avoid the Gibbs phenomenon, and the choice of technique depends on the specific application and signal characteristics.
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