Facial feature extraction using complex dual-tree wavelet transform
Computer Vision and Image Understanding
IEEE Transactions on Signal Processing
Optimization of the higher density discrete wavelet transform and of its dual tree
IEEE Transactions on Signal Processing
Design of Hilbert transform pairs of orthonormal wavelet bases using Remez exchange algorithm
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A new scheme for the design of Hilbert transform pairs of biorthogonal wavelet bases
EURASIP Journal on Advances in Signal Processing
A new algorithm based on complex wavelet transform for protein sequence classification
Proceedings of the International Conference on Advances in Computing, Communications and Informatics
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The condition on scaling filters of two orthogonal wavelet bases that render the corresponding wavelets as Hilbert transform pairs is re-examined in this note. Without making any pre-assumption on the relationship between the two scaling filters, the authors derive necessary and sufficient conditions for forming Hilbert transform pairs. They lead to new magnitude conditions and Selesnick's phase condition. Unique solutions to these conditions are concluded. It is shown that orthogonal wavelet bases form Hilbert transform pairs if and only if the two scaling filters are offset from one another by half a sample.