Hilbert pair of orthogonal wavelet bases: Revisiting the condition

IEEE Transactions on Signal Processing

Volumn 56, Issue 4, 2008, Pages 1716-1721

  Tay, David B H ^a  

^a LA TROBE UNIVERSITY   (Australia)

Author keywords

Complex wavelet; Dual tree; Hilbert pair; Orthonormal filter banks

Indexed keywords

FILTER BANKS; HILBERT SPACES; LOW PASS FILTERS; WAVELET ANALYSIS;

COMPLEX WAVELET; CONJUGATE QUADRATURE FILTERS; HILBERT PAIR;

SIGNAL FILTERING AND PREDICTION;

EID: 41849120502     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2007.909221     Document Type: Article

References (7)

1. I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, "The dual-tree complex wavelet transform," IEEE Signal Process. Mag., vol. 22, no. 6, pp. 123-151, Nov. 2005.
2. I. W. Selesnick, "Hilbert transform pairs of wavelet bases," IEEE Trans. Signal Proessc. Lett., vol. 8, no. 6, pp. 170-173, Jun. 2001.
3. H. Ozkaramanli and R. Yu, "On the phase condition and its solution for Hilbert transform pairs of wavelet bases," IEEE Trans. Signal Process., vol. 51, no. 12, pp. 3293-3294, Dec. 2003.
4. R. Yu and H. Ozkaramanli, "Hilbert transform pairs of orthogonal wavelet bases: Necessary and sufficient conditions," IEEE Trans. Signal Process., vol. 53, no. 12, pp. 4723-4725, Dec. 2005.
5. N. Kingsbury, "A dual-tree complex wavelet transform with improved orthogonality and symmetry properties," in Proc. IEEE Int. Conf. Image Processing (ICIP), 2000, vol. 2, pp. 375-378.
6. N. Kingsbury, "Design of Q-shift complex wavelets for image processing using frequency domain energy minimization," in Proc. IEEE Int. Conf. Image Processing (ICIP), 2003, vol. 1, pp. 1013-1016.
7. D. B. H. Tay, N. G. Kingsbury, and M. Palaniswami, "Orthonormal Hilbert pair of wavelets with (almost) maximum vanishing moments," IEEE Trans. Signal Process. Lett., vol. 13, no. 19, pp. 533-536, Sep. 2007.