A new non-redundant complex Hilbert wavelet transforms

In this paper, a novel non-redundant complex wavelet transform (NRCWT) for real-valued signals is proposed. For this purpose, an orthogonal complex filter bank is developed to implement this NRCWT. We show how to choose the two complex filters from classical real-valued wavelet filters in such a way that the filterbank is always orthogonal. Using fractional B-spline filters, a pair of exact Hilbert wavelets are constructed, which can separate the positive frequencies from the negative frequencies.