Design and application of Hilbert transform pairs of wavelet bases

A method for designing Hilbert transform pairs of orthogonal and biorthogonal wavelet bases was proposed, which can translate the problem into resolving algebraic equations via a flat fractional delay filter based on the sufficient and necessary condition for constructing wavelet. It avoids performing spectral factorization. Experiments show that the dual-tree complex wavelet transform (DT-CWT) based on the wavelet bases constructed by this method can more fit to extract features than the real discrete wavelet transform (DWT).