Directional dual-tree complex wavelet packet transforms for processing quadrature signals

  • Gorkem Serbes
  • Halil Ozcan Gulcur
  • Nizamettin AydinEmail author
Special Issue – Original Article


Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time–frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time–frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals.


Quadrature signal Complex wavelet packet transform Embolic signals Ultrasound 


  1. 1.
    Aydin N (1994) Computerised graft monitoring. Ph.D. dissertation, Dept. Med. Phys., University of Leicester, Leicester, UKGoogle Scholar
  2. 2.
    Aydin N, Evans DH (1994) Implementation of directional Doppler techniques using a digital signal processor. Med Biol Eng Comput 32:157–164CrossRefGoogle Scholar
  3. 3.
    Aydin N, Markus HS (2000) Directional wavelet transform in the context of complex quadrature Doppler signals. IEEE Signal Process Lett 10(7):278–280CrossRefGoogle Scholar
  4. 4.
    Aydin N, Markus HS (2001) Time-scale analysis of quadrature Doppler ultrasound signals. IEE Proc Sci Meas Technol 148(1):15–22CrossRefGoogle Scholar
  5. 5.
    Aydin N, Fan L, Evans DH (1994) Quadrature-to-directional format conversion of Doppler signals using digital methods. Physiol Meas 15:181–199CrossRefPubMedGoogle Scholar
  6. 6.
    Aydin N, Padayachee S, Markus HS (1999) The use of the wavelet transform to describe embolic signals. Ultrasound Med Biol 25(6):953–958CrossRefPubMedGoogle Scholar
  7. 7.
    Aydin N, Marvasti F, Markus HS (2004) Embolic Doppler ultrasound signal detection using discrete wavelet transform. IEEE Trans Inf Tech Biomed 8(2):182–190CrossRefGoogle Scholar
  8. 8.
    Bayram İ, Selesnick IW (2008) On the dual-tree complex wavelet packet and M-Band transforms. IEEE Trans Signal Process 56(6):2298–2310CrossRefGoogle Scholar
  9. 9.
    Brechet L, Lucas MF, Doncarli C, Farina D (2007) Compression of biomedical signals with mother wavelet optimization and best-basis wavelet packet selection. IEEE Trans Biomed Eng 54(12):2186–2192CrossRefPubMedGoogle Scholar
  10. 10.
    Coifman RR, Wickerhauser MV (1992) Entropy-based algorithms for best basis selection. IEEE Trans Inf Theory 38(2):713–718CrossRefGoogle Scholar
  11. 11.
    Gonçalves IB, Leiria A, Moura MMM (2013) STFT or CWT for the detection of Doppler ultrasound embolic signals. Int J Numer Methods Biomed Eng 29(9):964–976CrossRefGoogle Scholar
  12. 12.
    Jalobeanu A, Blanc-Féraud L, Zerubia J (2000) Satellite image deconvolution using complex wavelet packets. In: Proceedings of IEEE international conference on image processing (ICIP), 2000Google Scholar
  13. 13.
    Jalobeanu A, Kingsbury N, Zerubia J (2001) Image deconvolution using hidden Markov tree modeling of complex wavelet packets. In: Proceedings of IEEE international conference on image processing (ICIP), pp 201–204Google Scholar
  14. 14.
    Jalobeanu A, Blanc-Féraud L, Zerubia J (2003) Satellite image deblurring using complex wavelet packets. Int J Comput Vis 51(3):205–217CrossRefGoogle Scholar
  15. 15.
    Khushaba RN, Kodagoda S, Lal S, Dissanayake G (2011) Driver drowsiness classification using fuzzy wavelet-packet-based feature-extraction algorithm. IEEE Trans Biomed Eng 58(1):121–131CrossRefPubMedGoogle Scholar
  16. 16.
    Kingsbury NG (1999) Shift invariant properties of the dual-tree complex wavelet transform. In: Proceedings of IEEE conference on acoustics, speech and signal processing, Phoenix, AZ, pp 1221–1224Google Scholar
  17. 17.
    Kingsbury NG (2001) Complex wavelets for shift invariant analysis and filtering of signals. J Appl Comput Harmonic Anal 10(3):234–253CrossRefGoogle Scholar
  18. 18.
    Lyons RG (2010) Understanding digital signal processing, 3rd edn. Prentice Hall, Englewood CliffsGoogle Scholar
  19. 19.
    Mallat S (1998) A wavelet tour of signal processing. Academic Press, San DiegoGoogle Scholar
  20. 20.
    Marvasti S, Gillies D, Marvasti F, Markus HS (2004) Online automated detection of cerebral embolic signals using a wavelet based system. Ultrasound Med Biol 30(5):647–653CrossRefPubMedGoogle Scholar
  21. 21.
    Oppenheim AV, Schafer RW, Buck JR (1999) Discrete-time signal processing. Prentice-Hall, Englewood CliffsGoogle Scholar
  22. 22.
    Ozkaramanli H, Yu R (2003) On the phase condition and its solution for Hilbert transform pairs of wavelet bases. IEEE Trans Signal Process 51(12):3293–3294CrossRefGoogle Scholar
  23. 23.
    Ramchandran K, Vetterli M (1993) Best wavelet packet basis in a rate-distortion sense. IEEE Trans Image Process 2(2):160–175CrossRefPubMedGoogle Scholar
  24. 24.
    Ravier P, Amblard PO (2001) Wavelet packets and de-noising based on higher-order-statistics for transient detection. Sig Process 81(9):1909–1926CrossRefGoogle Scholar
  25. 25.
    Roy E, Abraham P, Montrésor S, Baudry M, Saumet JL (1998) The narrow band hypothesis: and interesting approach for high-intensity signals (HITS) detection. Ultrasound Med Biol 24(3):375–382CrossRefPubMedGoogle Scholar
  26. 26.
    Selesnick IW (2001) Hilbert transform pairs of wavelet bases. IEEE Signal Process Lett 8(6):170–173CrossRefGoogle Scholar
  27. 27.
    Selesnick IW, Baraniuk RG, Kingsbury NG (2005) The dual-tree complex wavelet transform. IEEE Signal Process Mag 22(6):123–151CrossRefGoogle Scholar
  28. 28.
    Serbes G (2009) Analysis of quadrature Doppler signals with a modified dual-tree complex wavelet transform. Master’s thesis, Bahcesehir University, Istanbul, TurkeyGoogle Scholar
  29. 29.
    Serbes G, Aydin N (2009) A complex discrete wavelet transform for processing quadrature Doppler ultrasound signals. In: 9th international conference on information technology and applications in biomedicine ITAB 2009Google Scholar
  30. 30.
    Serbes G, Aydin N (2011) Modified dual tree complex wavelet transform for processing quadrature signals. Biomed Signal Process Control 6(3):301–306CrossRefGoogle Scholar
  31. 31.
    Serbes G, Aydin N (2011) Symmetrical modified dual tree complex wavelet transform for processing quadrature Doppler ultrasound signals. Engineering in Medicine and Biology Society, EMBC, 2011 annual international conference of the IEEE, pp 4816–4819Google Scholar
  32. 32.
    Serbes G, Aydin N (2014) Denoising performance of modified dual-tree complex wavelet transform for processing quadrature embolic Doppler signals. Med Biol Eng Comput 52(1):29–43CrossRefPubMedGoogle Scholar
  33. 33.
    Vautrin D, Artusi X, Lucas MF, Farina D (2009) A novel criterion of wavelet packet best basis selection for signal classification with application to brain-computer interfaces. IEEE Trans Biomed Eng 56(11):2734–2738CrossRefPubMedGoogle Scholar
  34. 34.
    Weickert T, Benjaminsen C, Kiencke U (2009) Analytic wavelet packets—combining the dual-tree approach with wavelet packets for signal analysis and filtering. IEEE Trans Signal Process 57(2):493–502CrossRefGoogle Scholar
  35. 35.
    Xie Z, Wang E, Zhang G, Zhao G, Chen X (2004) Seismic signal analysis based on the dual-tree complex wavelet packet transform. Acta Seismol Sin 17(1):117–122CrossRefGoogle Scholar
  36. 36.
    Yu R, Ozkaramanli H (2005) Hilbert transform pairs of orthogonal wavelet bases: necessary and sufficient conditions. IEEE Trans Signal Process 53(12):4723–4725CrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2014

Authors and Affiliations

  • Gorkem Serbes
    • 1
  • Halil Ozcan Gulcur
    • 2
  • Nizamettin Aydin
    • 3
    Email author
  1. 1.Biomedical Engineering DepartmentBahcesehir UniversityBesiktas, IstanbulTurkey
  2. 2.Biomedical Engineering InstituteBogazici UniversityKandilli, IstanbulTurkey
  3. 3.Computer Engineering Department, Faculty of Electrical and ElectronicsYildiz Technical UniversityIstanbulTurkey

Personalised recommendations