Design of Hilbert transform pairs of orthonormal wavelet bases with improved analyticity

This paper proposes a class of Hilbert transform pairs of orthonormal wavelet bases with improved analyticity. To improve the analyticity of complex wavelet, a different allpass filter is used for the half-sample delay approximation. We present a design method for allpass filters with the specified degree of flatness at ω = 0 and equiripple phase response in the approximation band. Remez exchange algorithm is applied in the approximation band, and then a set of filter coefficients can be obtained easily by solving the eigenvalue problem. Therefore, the equiripple phase response is attained through a few iterations. Furthermore, the corresponding filter banks are constructed from the designed allpass filters by using the method proposed in [7]. The resulting orthonormal wavelet bases possess the maximum number of vanishing moments. Finally, one example is presented to demonstrate the improvement of the analyticity.

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