Reduced Complexity Discrete Hilbert Transform Calculation for Finite Length Sequences

Year 2025, Volume: 22 Issue: 2, 116 - 120, 01.11.2025

Orhan Gazi

https://izlik.org/JA74YR92JE

Abstract

Hilbert transform is a well-known transform method used in communication systems. In this paper, we propose novel methods for the calculation of discrete Hilbert transform using matrix multiplication. The proposed method has reduced complexity, and it can be used for hardware implementations. Besides, we propose simple methods for the generation of Hilbert transform submatrices used in DHT operation. The proposed approaches can be used in hardware implementations.

Keywords

Discrete Hilbert transform , Reduced complexity , Matrix Decomposition

References

• S. Kak, "The discrete Hilbert transform," Proc. IEEE, vol. 58, pp. 585-586, Apr. 1970, doi: 10.1109/PROC.1970.7696.
• V. Cizek, "Discrete Hilbert transform," IEEE Trans. Speech Audio Process, vol. 18, issue: 4, pp. 340 – 343, Dec. 1970, doi: 10.1109/TAU.1970.1162139.
• S. Kak, "Hilbert transformation for discrete data, " Int. J. Electron., pp. 177-183, 1973, doi: 10.1080/00207217308938428.
• M. Sabri, W. Steenaart, "Discrete Hilbert transform filtering, " IEEE Trans. Acoust., Speech, Signal. Process., vol. 25, issue: 5, pp. 452 – 454, Oct.1977, doi: 10.1109/ICASSP.1976.1170068.
• R. Ansari, "IIR discrete-time Hilbert transformers," IEEE Trans., ASSP-33, pp. 1146-1150, Aug.1985, doi: 10.1109/TASSP.1987.1165250.
• S. L. Hahn, "Hilbert Transforms," Transforms and Applications Handbook, A. D. Poularikas, Ed., CRC Press Inc., Boca Raton, FL, 1996.
• R. Tao, X. Li, Y. Wang, "Generalization of the fractional Hilbert transform," IEEE Signal Process. Lett., vol. 15, pp. 365 – 368, Dec. 2008, doi: 10.1109/LSP.2008.919814.
• S.C. Pei, M.H. Yeh, "Discrete fractional Hilbert transform," IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process, vol. 47, issue: 11, Dec.2000, doi: 10.1109/82.885138.
• P. S. Reddy, S. Mopuri, A. Acharyya, "A Reconfigurable high speed architecture design for discrete Hilbert transform," IEEE Signal Process. Lett., vol. 21, issue. 11, pp. 1413 – 1417, Nov. 2014, doi: 10.1109/LSP.2014.2333745.
• L. Liu, Y. Zhang, "Design and Implementation of Reconfigurable Discrete Hilbert Transform Based on Systolic-Arrays," presented at the CMC 2010, Shenzhen, China, Apr. 12-14, 2010, pp.245-249.
• R. Sun, Y. Zhang, J. Chen, "The configurable structure for discrete Hilbert Transform via systolic array," presented at the ICIS 2025 (IEEE), Niigata, Japan, Jun. 16-20, 2013, pp. 467-473.
• S.C. Pei, S.B. Jaw, "Computation of discrete Hilbert transform through fast Hartley transform," IEEE Trans. Circuits Syst., vol. 36, issue. 9, pp. 1251 – 1252, Sept. 1989, doi: 10.1109/31.34675.
• M.Pushpalatha, "Design of Low Complexity Nonrecursive Fractional Hilbert Transformer," presented at the ICMACC 2022, Hyderabad, India, Dec. 28-30, 2022, pp.1-5.
• P. Waskito, S. Miwa, Y. Mitsukura, H, Nakajo, "Parallelizing Hilbert-Huang Transform on a GPU," presented at the ICNDC 2010, Higashi, Japan, Nov. 17-19, 2010, pp. 184-190.
• E. Hermanowicz, A. Paruzel, "Farrow structure for complex digital Hilbert filter of low complexity," presented at the SPA 2007, Poznan, Poland, Sept. 7-7, 2007, pp.91-96.