Complex Hilbert Transform Filter

References

[1] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, E. H. Shih, Q. Zheng, C. C. Tung and H. H. Liu, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis,” Pro- ceedings of the Royal Society of London A, Vol. 454, No. 1971, 1998, pp. 903-995.

[2]
I. W. Selesnick, “Hilbert Transform Pairs of Wavelet Bases,” IEEE Signal Processing Letters, Vol. 8, No. 6, 2001, pp. 170-173. doi:10.1109/97.923042

[3]
H. Ozkaramanli and R. Yu, “On the Phase Condition and Its Solution for Hilbert Transform Pairs of Wavelet Bases,” IEEE Transactions on Signal Processing, Vol. 51, No. 12, 2003, pp. 3293-3294.
doi:10.1109/TSP.2003.818996

[4]
R. Yu and H. Ozkaramanli, “Hilbert Transform Pairs of Biorthogonal Wavelet Bases,” IEEE Transactions on Signal Processing, Vol. 54, No. 6, 2006, pp. 2119-2125.
doi:10.1109/TSP.2006.874293

[5]
H. Olkkonen, J. T. Olkkonen and P. Pesola, “FFT Based Computation of Shift Invariant Analytic Wavelet Transform,” IEEE Signal Processing Letters, Vol. 14, No. 3, 2007, pp. 177-180. doi:10.1109/LSP.2006.879983

[6]
W. M. Moon, A. Ushah and B. Bruce, “Application of 2-D Hilbert Transform in Geophysical Imaging with Potential Field Data,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 26, No. 5, 1988, pp. 502-510.
doi:10.1109/36.7674

[7]
H. Olkkonen, P. Pesola, J. T. Olkkonen and H. Zhou, “Hilbert Transform Assisted Complex Wavelet Transform for Neuroelectric Signal Analysis,” Journal of Neuroscience Methods, Vol. 151, No. 2, 2006, pp. 106-113.
doi:10.1016/j.jneumeth.2005.06.028

[8]
H. Kanai, Y. Koiwa and J. Zhang, “Real-Time Measurements of Local Myocardium Motion and Arterial Wall Thickening,” IEEE Transaction on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 46, No. 5, 1999, pp. 1229-1241. doi:10.1109/58.796128

[9]
S. M. Shors, A. V. Sahakian, H. J. Sih and S. Swiryn, “A Method for Determining High-Resolution Activation Time Delays in Unipolar Cardiac Mapping,” IEEE Tran- saction on Biomedical Engineering, Vol. 43, No. 12, 1996, pp. 1192-1196.

[10]
A. K. Barros and N. Ohnishi, “Heart Instantaneous Frequency (HIF): An Alternative Approach to Extract Heart Rate Variability,” IEEE Transaction on Biomedical Engineering, Vol. 48, No. 8, 2001, pp. 850-855.
doi:10.1109/10.936361

[11]
O. W. Kwon and T. W. Lee, “Phoneme Recognition Using ICA-Based Feature Extraction and Transformation,” Signal Processing, Vol. 84, No. 6, 2004, pp. 1005-1019.
doi:10.1016/j.sigpro.2004.03.004

[12]
A. V. Oppenheim and R. W. Schafer, “Discrete-Time Signal Processing,” Prentice-Hall, Englewood Cliffs, NJ, 1989.

[13]
A. Rao and R. Kumaresan, “A Parametric Modeling Approach to Hilbert Transformation,” IEEE Signal Proces- sing Letters, Vol. 5, No. 1, 1998, pp. 15-17.
doi:10.1109/97.654868

[14]
R. Kumaresan, “An Inverse Signal Approach to Computing the Envelope of a Real Valued Signal,” IEEE Signal Processing Letters, Vol. 5, No. 10, 1998, pp. 256-259.
doi:10.1109/97.720558

[15]
K. L. Peacock, “Kaiser-Bessel Weighting of the Hilbert Transform High-Cut Filter,” IEEE Transaction on Acoustics, Speech, and Signal Analysis, Vol. 33, No. 1, 1985, pp. 329-331. doi:10.1109/TASSP.1985.1164514

[16]
J. T. Olkkonen and H. Olkkonen, “Fractional Delay Filter Based on the B-Spline Transform,” IEEE Signal Proces- sing Letters, Vol. 14, No. 2, 2007, pp. 97-100.
doi:10.1109/LSP.2006.882103

[17]
T. Laakso, V. Valimaki, M. Karjalainen and U. K. Laine, “Splitting the Unit Delay. Tools for Fractional Delay Filter Design,” IEEE Signal Processing Magazine, Vol. 13, No. 1, 1996, pp. 30-60. doi:10.1109/79.482137

[18]
S. C. Pei and C. C. Tseng, “An Efficient Design of a Variable Fractional Delay Filter Using a First-Order Differentiator,” IEEE Signal Processing Letters, Vol. 10, No. 10, 2003, pp. 307-310. doi:10.1109/LSP.2003.815616

[19]
S. C. Pei and P. H. Wang, “Closed-Form Design of All-Pass Fractional Delay,” IEEE Signal Processing Letters, Vol. 11, No. 10, 2004, pp. 788-791.
doi:10.1109/LSP.2004.835473

[20]
H. Johansson and P. Lowenborg, “Reconstruction of Nonuniformly Sampled Bandlimited Signals by Means of Digital Fractional Delay Filters,” IEEE Transaction on Signal Processing, Vol. 50, No. 11, 2002, pp. 2757-2767.
doi:10.1109/TSP.2002.804089

[21]
C. C. Tseng, “Digital Integrator Design Using Simpson Rule and Fractional Delay Filter,” IEE Proceedings of Vision, Image and Signal Processing, Vol. 153, No. 1, 2006, pp. 79-85. doi:10.1049/ip-vis:20045208

[22]
M. Unser, A. Aldroubi and M. Eden, “Polynomial Spline Approximations: Filter Design and Asymptotic Equivalence with Shannon’s Sampling Theorem,” IEEE Transactions on Information Theory, Vol. 38, No. 1, 1992, pp. 95-103. doi:10.1109/18.108253