I've recently been looking into wavelet analysis and I have the question: What is the importance of wavelets having an orthogonal basis, say as opposed to a bi-orthogonal basis or otherwise? I'm fairly new to a lot of functional analysis so I've not seen the importance of this property so far in what I've researched. Many thanks.
2026-03-25 17:26:07.1774459567
Significance of orthonormal basis in wavelet analysis
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Orthogonal wavelets allows for analysis and synthesis filters to be the same and only one filter (and it's mirrored alternating signs). For biorthogonal wavelets you need two different filters and their respective mirrored alternating signs. So you have more degrees of freedom in designing biorthogonal wavelets, although the implementation will be slightly more complicated.