Skip to main content
SpringerLink
Log in

Design of IIR Multiple-Notch Filters with Symmetric Magnitude Responses About Notch Frequencies

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

A novel all-pass-based infinite impulse response (IIR) digital multiple-notch filter design method is presented in this paper. The proposed method ensures that, for an arbitrary pass-bands ripple value, specifications regarding positions of notch, left- and right-hand cutoff frequencies are exactly met, which leads to symmetric magnitude responses about notch frequencies. Although iterative in its nature, proposed method requires a small number of iterations to find coefficients of the multiple-notch filter, making it very useful for designers. Since the magnitude response of the all-pass-based IIR multiple-notch filter is more sensitive in the stop-bands than in the pass-bands, sensitivity analysis along with simulation in limited word-length environment is performed.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. D. Borio, L. Camoriano, L.L. Presti, Two-pole and multi-pole notch filters: a computationally effective solution for GNSS interference detection and mitigation. IEEE Syst. J. 2(1), 38–47 (2008)

    Article  Google Scholar 

  2. J.A. Cadzow, Minimum \(l_1\), \(l_2\), and \(l_{\infty }\) norm approximate solutions to an overdetermined system of linear equations. Digit. Signal Proc. 12(4), 524–560 (2002)

    Article  Google Scholar 

  3. C. Duarte, K.E. Barner, K. Goossen, Design of IIR multi-notch filters based on polynomially-represented squared frequency response. IEEE Trans. Signal Process. 64(10), 2613–2623 (2016)

    Article  MathSciNet  Google Scholar 

  4. Y. Jiang, C. Shen, J. Dai, A unified approach to the design of IIR and FIR notch filters, in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2016), pp. 4791–4795

  5. Y.D. Jou, Z.P. Lin, F.K. Chen, Interference elimination of electrocardiogram signals using IIR multiple notch filters, in 2016 IEEE 5th Global Conference on Consumer Electronics (2016), pp. 1–2

  6. G. Jovanovic-Dolecek, S.K. Mitra, Symbolic sensitivity analysis of digital filter structures using MATLAB, in 9th International Conference on Electronics, Circuits and Systems, vol 3 (2002), pp. 903–906

  7. S. Nikolić, G. Stančić, Design of IIR notch filter with approximately linear phase. Circuits Syst. Signal Process, 31(6), 2119–2131 (2012). https://doi.org/10.1007/s00034-012-9426-x

    Article  MathSciNet  Google Scholar 

  8. K. Nikolova, G. Stoyanov, M. Kawamata, Low-sensitivity design and implementation of allpass based fractional delay digital filters, in 2009 European Conference on Circuit Theory and Design (2009), pp. 603–606

  9. S.C. Pei, C.C. Tseng, IIR multiple notch filter design based on allpass filter, in TENCON ’96. Proceedings, 1996 IEEE TENCON. Digital Signal Processing Applications, vol 1 (1996), pp. 267–272

  10. S.C. Pei, C.C. Tseng, IIR multiple notch filter design based on allpass filter. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 44(2), 133–136 (1997)

    Article  Google Scholar 

  11. J.R. Rice, Numerical Methods, Software, and Analysis, 2nd edn. (Academic Press, Cambridge, 1993)

    MATH  Google Scholar 

  12. K. Song, Q. Xue, Asymmetric dual-line coupling structure for multiple-notch implementation in UWB bandpass filters. Electron. Lett. 46(20), 1388–1390 (2010)

    Article  Google Scholar 

  13. G. Stančić, S. Nikolić, Digital linear phase notch filter design based on IIR all-pass filter application. Digit. Signal Process. Rev. J. 23(3), 1065–1069 (2013)

    Article  MathSciNet  Google Scholar 

  14. G. Stoyanov, H. Clausert, A comparative study of first-order digital allpass filter sections. Frequenz 48, 221–226 (1994)

    Article  Google Scholar 

  15. G. Stoyanov, Z. Nikolova, K. Ivanova, V. Anzova, Design and realization of efficient IIR digital filter structures based on sensitivity minimizations, in 2007 8th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Services (2007), pp. 299–308

  16. G. Stoyanov, K. Nikolova, M. Kawamata, Low-Sensitivity Design of Allpass Based Fractional Delay Digital Filters, in Digital Filters, ed. by Fausto Pedro García Márquez (InTech, Croatia, 2011), pp. 155–178

    Google Scholar 

  17. L. Tan, J. Jiang, L. Wang, Pole-radius-varying IIR notch filter with transient suppression. IEEE Trans. Instrum. Meas. 61(6), 1684–1691 (2012)

    Article  Google Scholar 

  18. A. Thamrongmas, C. Charoenlarpnopparut, All-pass based IIR multiple notch filter design using Gröbner Basis, in 7th International Workshop on Multidimensional (nD) Systems (nDs) (IEEE, 2001), pp. 1–6

  19. A. Thamrongmas, C. Charoenlarpnopparut, P. Prempree, A novel design of IIR multiple notch filter based on an all-pass filter by using a pole-reposition technique. SCIENCEASIA 40(5), 362–370 (2014)

    Article  Google Scholar 

  20. C.C. Tseng, S.C. Pei, Stable IIR notch filter design with optimal pole placement. IEEE Trans. Signal Process. 49(11), 2673–2681 (2001)

    Article  MathSciNet  Google Scholar 

  21. Q. Wang, D. Kundur, A generalized design framework for IIR digital multiple notch filters. EURASIP J. Adv. Signal Process. 2015(1), 1–26 (2015)

    Article  Google Scholar 

  22. Q. Wang, J. Song, H. Yuan, Digital Multiple Notch Filter Design Based on Genetic Algorithm, in 2014 Fourth International Conference on Instrumentation and Measurement, Computer, Communication and Control (2014), pp. 180–183

  23. X.L. Wang, Y.J. Ge, J.J. Zhang, Q.J. Song, Discussion on the \(-\)3 dB rejection bandwidth of IIR notch filters, in 6th International Conference on Signal Processing, vol 1 (2002), pp. 151–154

Download references

Author information

Authors and Affiliations

  1. Faculty of Technical Sciences, University of Priština, Knjaza Miloša 7, 38220, Kosovska Mitrovica, Serbia

    Ivan Krstić & Predrag Lekić

  2. Faculty of Electronic Engineering, University of Niš, Aleksandra Medvedeva 14, 18000, Niš, Serbia

    Saša Nikolić & Goran Stančić

Authors
  1. Ivan Krstić
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saša Nikolić
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Goran Stančić
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Predrag Lekić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivan Krstić.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krstić, I., Nikolić, S., Stančić, G. et al. Design of IIR Multiple-Notch Filters with Symmetric Magnitude Responses About Notch Frequencies. Circuits Syst Signal Process 37, 5616–5636 (2018). https://doi.org/10.1007/s00034-018-0841-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-018-0841-5

Keywords

Search

Navigation