Skip to main content
SpringerLink
Log in

Design of Two Channel Biorthogonal Filterbanks using Euler Frobenius Polynomial

  • Published:
Journal of Signal Processing Systems Aims and scope Submit manuscript

Abstract

This paper presents a technique to design a new class of biorthogonal perfect reconstruction (PR) filterbanks. In this technique, we use Euler Frobenius polynomial (EFP) to design maximally flat Euler Frobenius halfband polynomial (EFHP). This is obtained by imposing vanishing moments (VMs) and PR constraints on EFP. The resulted EFHP is used in three and four step lifting structure to determine analysis low-pass and high-pass filters. The lifting halfband kernels are designed using EFHP. It has been ensured that the proposed filters satisfy the linear phase and PR property. Also, the proposed filters have frame bound ratio very close to unity. Several design examples are presented and the properties of proposed filters are compared with existing filters. It has been ensured that the proposed filters give more regularity as compared to existing filterbanks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9

Similar content being viewed by others

References

  1. Strang, G., & Nguyen, T. (1996). Wavelets and Filter Banks. Wellesley-cambridge, NY.

  2. Vaidyanathan, P.P. (1993). Multirate Systems and Filter banks. Englewood Cliffs Prentice-Hall, NJ.

  3. Rahulkar, A.D., & Holambe, R.S. (2014). Iris Image Recognition- Wavelet Filter-banks Based Iris Feature Extraction Schemes. SpringerBriefs in Signal Processing.

  4. Vetterli, M., & Kovacevic, J. (1995). Wavelets and Subband Coding. Englewood cliffs Prentice-Hall, NJ.

  5. Naik, A.K., & Holambe, R.S. (2013). Design of low-complexity high-performance wavelet filters for image analysis. IEEE Transactions on Image Processing, 22(5), 1848–1858. ISSN 1057-7149. https://doi.org/10.1109/TIP.2013.2237917.

    Article  MathSciNet  Google Scholar 

  6. Patil, B., Patwardhan, P., Gadre, V. (2008). On the design of FIR wavelet filter banks using factorization of a halfband polynomial. IEEE Signal Processing Letters, 15, 485–488.

    Article  Google Scholar 

  7. Patil, B., Patwardhan, P., Gadre, V. (2008). Eigenfilter approach to the design of one-dimensional and multidimensional two-channel linear phase FIR perfect reconstruction filter banks. IEEE Transactions on Circuit and Systems Vol-I.

  8. Tay, D.B.H. (2000). Rationalizing the coefficients of popular biorthogonal wavelet filters. IEEE Transactions on Circuits and Systems for Video Technology, 10(6), 998–1005. ISSN 1051-8215. https://doi.org/10.1109/76.867939.

    Article  Google Scholar 

  9. Murugesan S., & Tay, D.B.H. (2012). New techniques for rationalizing orthogonal and biorthogonal wavelet filter coefficients. IEEE Transactions on Circuits and Systems I: Regular Papers, 59(3), 628–637. ISSN 1549-8328. https://doi.org/10.1109/TCSI.2011.2165415.

    Article  MathSciNet  Google Scholar 

  10. Tay, D.B.H., & Lin, Z. (2018). Almost tight rational coefficients biorthogonal wavelet filters. IEEE Signal Processing Letters, 25(6), 748–752. ISSN 1070-9908. https://doi.org/10.1109/LSP.2018.2819971.

    Article  Google Scholar 

  11. Naik, A.K., & Holambe, R.S. (2014). New approach to the design of low complexity 9/7 tap wavelet filters with maximum vanishing moments. IEEE Transactions on Image Processing, 23(12), 5722–5732. ISSN 1057-7149. https://doi.org/10.1109/TIP.2014.2363733.

    Article  MathSciNet  Google Scholar 

  12. Naik, A.K., & Holambe, R.S. (2017). A unified framework for the design of low-complexity wavelet filters. International Journal of Wavelets, Multiresolution and Information Processing, 15(6), 1–27. https://doi.org/10.1142/S0219691317500540.

    Article  MathSciNet  MATH  Google Scholar 

  13. Gawande, J.P., Rahulkar, A.D., Holambe, R.S. (2016). A new approach to design triplet halfband filter banks based on balanced-uncertainty optimization. Digital Signal Processing, 56, 123–131. ISSN 1051-2004. https://doi.org/10.1016/j.dsp.2016.06.001.

    Article  MathSciNet  Google Scholar 

  14. Nagare, M.B., Patil, B.D., Holambe, R.S. (2016). Design of two-dimensional quincunx fir filter banks using eigen filter approach. In 2016 International Conference on Signal and Information Processing (IConSIP) (pp. 1–5). https://doi.org/10.1109/ICONSIP.2016.7857452.

  15. Nagare, M.B., Patil, B.D., Holambe, R.S. (2016). A multi directional perfect reconstruction filter bank designed with 2-d eigenfilter approach: Application to ultrasound speckle reduction. Journal of Medical Systems, 41 (2), 31. ISSN 1573-689X. https://doi.org/10.1007/s10916-016-0675-2.

    Article  Google Scholar 

  16. Rahulkar, A.D., & Holambe, R.S. (2012). Partial iris feature extraction and recognition based on a new combined directional and rotated directional wavelet filter banks. Neurocomputing, 81, 12–23.

    Article  Google Scholar 

  17. Tay, D.B.H., & Palaniswami, M. (2004). A novel approach to the design of the class of triplet halfband filterbanks. IEEE Transactions on Circuits Systems and Systems-II:Express Brief, 51(7), 378–383.

    Article  Google Scholar 

  18. Tkacenko, A., Vaidyanathan, P.P., Nguyen, T. (2003). On the eigenfilter design method and its applications: a tutorial. IEEE Transaction on Circuits and Systems, 50, 497–517.

    Google Scholar 

  19. Daubechies, I. (1992). Ten Lectures on Wavelets. Philadelphia: SIAM.

    Book  Google Scholar 

  20. Daubechies, I., & Feauveau, J. (1992). Biorthogonal bases of compactly supported wavelets. Communication Pure Appllied Mathematics, (45):485–560.

  21. Ansari, R., Kaiser, C., Guillemot, J. (1991). Wavelet construction using lagrange halfband filters. IEEE Transaction on Circuits and Systems:Express Brief, 38(9), 1116–1118.

    Article  Google Scholar 

  22. Phoong, S., Kim, C., Vaidyanathan, P., Ansari, R. (1995). A new class of two-channel biorthogonal filter banks and wavelet bases. IEEE Transactions on Signal Processing, 43(3), 649–665.

    Article  Google Scholar 

  23. Ansari, R., Kim, C.W., Dedovic, M. (1999). Structure and design of two-channel filter banks derived from a triplet of halfband filters. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 46 (12), 1487–1496. ISSN 1057-7130. https://doi.org/10.1109/82.809534.

    Article  Google Scholar 

  24. Chui, C.K. (1992). An introduction to wavelets. Academic Press.

  25. Tay, D.B.H., & Lin, Z. (2016). Biorthogonal filter banks constructed from four halfband filters. In 2016 IEEE International symposium on circuits and systems (ISCAS) (pp. 1222–1225). https://doi.org/10.1109/ISCAS.2016.7527467.

  26. Shapiro, J.M. (1993). Embedded image coding using zerotrees of wavelet coefficients. IEEE Transactions on Signal Processing, 41(12), 3445–3462. ISSN 1053-587X, https://doi.org/10.1109/78.258085.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. works with Department of Instrumentation Engineering, Ramrao Adik Institute of Technology, Navi Mumbai and SGGS Institute of Engineering and Technology, Nanded, India

    Mukund B. Nagare

  2. Philips Healthcare Innovation Centre, Pune, India

    Bhushan D. Patil

  3. Department of Instrumentation Engineering, SGGS Institute of Engineering and Technology, Nanded, India

    Raghunath S. Holambe

Authors
  1. Mukund B. Nagare
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bhushan D. Patil
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raghunath S. Holambe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mukund B. Nagare.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nagare, M.B., Patil, B.D. & Holambe, R.S. Design of Two Channel Biorthogonal Filterbanks using Euler Frobenius Polynomial. J Sign Process Syst 92, 611–619 (2020). https://doi.org/10.1007/s11265-019-01515-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11265-019-01515-z

Keywords

Search

Navigation