Do there exists wavelets such that both mother wavelet and the scaling function have compact support and they are both twice continuously differentiable?
2026-03-25 02:57:15.1774407435
Twice continuously differentiable wavelets with compact support
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Yes, I believe that Daubechies Wavelets of high orders satisfy this.
Daubechies Wavelets have a compact support (that's why they were invented), and the higher the order, the higher the regularity.
This doc relates the order of the Daubechies Wavelets (and scaling functions) with their Holder exponent. It seems that at order 7, both wavelets and scaling functions are of holder exponent $\geq 2$, which implies that they're both twice continuously differentiable.