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The Hilbert Transforms of Complex Shannon Wavelet and Marr Wavelet

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DOI: 10.23977/jfer.2021.010217 | Downloads: 1 | Views: 54

Author(s)

YANG Xiuzhu 1

Affiliation(s)

1 College of Science, China Three Gorges University, Yichang 443002, China

Corresponding Author

YANG Xiuzhu

ABSTRACT

The Hilbert transform of complex Shannon wavelet is firstly calculated by using the Residue Theorem. The Hilbert transform of Marr wavelet is then computed by applying the Hilbert transform of Gaussian functions. Since these two kinds of wavelets are relatively important in practice, the calculation of the Hilbert transforms of these two kinds of wavelets could be useful for designing of the wavelets which form a pair of Hilbert transform.

KEYWORDS

Shannon wavelet, Marr wavelet, Hilbert transform

CITE THIS PAPER

YANG Xiuzhu, The Hilbert Transforms of Complex Shannon Wavelet and Marr Wavelet. Journal of Frontiers in Educational Research (2021) 1: 72-75. DOI: http://dx.doi.org/10.23977/jfer.2021.010217

REFERENCES

[1] C. CATTANI, Shannon Wavelets Theory[J], Mathematical Problems in Engineering, 2008.
[2] C. CATTANI, Shannon Wavelets for the Solution of Integrodifferential Equations[J], Mathematical Problems
[3] in Engineering, 2010.
[4] Shi Xiaofeng, Gu Haiyan, Ma Xiaojian, Application of Marr Wavelet to Hydrology [J], Journal of Northeast
[5] Forestry University, 2008, vol. 36 No. 6, pp. 96-97.
[6] H. OZKARAMANL, R. Yu, On the phase condition and its solution for Hilbert transform pairs of wavelet bases[J],
[7] IEEE Transactions on Signal Processing, 2003, vol. 51 No.12, pp. 3293-3294.
[8] R. YU, H. OAKARAMANL, Hilbert transform pairs of biorthogonal wavelet bases[J], IEEE Transactions on Signal
[9] Processing, 2006, vol. 54 No. 6, pp. 2119-2125.
[10] Chen Zhongying, Wu Bin, Wavelet Analysis[M], Science Press, Beijing, 2007, pp. 132.
[11] BURTON D. Fried, SAMUEL D. Conte., The plasma dispersion function: The Hilbert transform of the Gaussian[M], Academic Press, 1961.

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