Fractional Hilbert Transforms of Biorthogonal Wavelets

We show that the fractional Hilbert transform preserves the biorthogonal wavelet property. For a naturally generated biorthogonal wavelet pair constructed from a given biorthogonal scaling pair, we propose a design to construct a better biorthogonal scaling pair for the naturally generated biorthogonal wavelet pair using the fractional Hilbert transform. We also propose a calculation method for low-pass and high-pass filters.