Design of nearly linear-phase double notch digital filters with close notch frequencies

Design of nearly linear-phase double notch digital filters with close notch frequencies

For access to this article, please select a purchase option:

Buy article PDF
(plus tax if applicable)
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
IET Signal Processing — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

In this study, the authors present a new procedure for the synthesis of the nearly linear-phase infinite impulse response (IIR) filters with two close notch frequencies based on all-pass filter application. The filter is obtained using a parallel connection of the delay line and IIR all-pass filter with a piecewise approximately linear phase. The desired magnitude characteristic is achieved by equiripple approximation of the all-pass filter phase. The magnitude characteristic is equiripple in all passbands. The proposed method is also suitable for the synthesis of complementary filters for extraction of the signal components at prescribed frequencies. The initial solution for the arbitrary order of an all-pass filter is proposed, which attains a sufficient number of phase error extrema. All phase error minima and maxima corresponding to the initial solution have almost identical values, excluding the ones near notch frequencies. As a result, the method exhibits fast and strong convergence. The described method can also be applied for the design of multiple notch filters with two very close notch frequencies.


    1. 1)
      • 1. Proakis, J.G., Manolakis, D.G.: ‘Digital signal processing principle, algorithms, and applications’ (Prentice-Hall, Upper Saddle River, New Jersey, USA, 1996).
    2. 2)
      • 2. Mitra, S.K.: ‘Digital signal processing: a computer based approach’ (McGraw-Hill, New York, 2006, 3rd edn.).
    3. 3)
      • 3. Chien-Cheng, T., Soo-Chang, P.: ‘Stable IIR notch filter design with optimal pole placement’, IEEE Trans. Signal Process., 2001, 49, pp. 26732681.
    4. 4)
      • 4. Saramaki, T.: ‘On the design of digital filters as a sum of two all-pass filters’, IEEE Trans. Circuits Syst., 1985, 32, pp. 11911193.
    5. 5)
      • 5. Vaidyanathan, P.P., Mitra, S.K., Neuvo, Y.: ‘A new approach to the realization of low sensitivity IIR digital filters’, IEEE Trans. Acoust. Speech Signal Process., 1986, 34, pp. 350361.
    6. 6)
      • 6. Nikolić, S., Stančić, G.: ‘Design of IIR notch filter with approximately linear phase’, Circuits Syst. Signal Process., 2012, 31, (6), pp. 21192131.
    7. 7)
      • 7. Stančić, G., Nikolić, S.: ‘Digital linear phase notch filter design based on IIR all-pass filter application’, Digit. Signal Process., 2013, 23, pp. 10651069.
    8. 8)
      • 8. Stančić, G., Nikolić, S.: ‘Design of digital recursive notch filter with linear phase characteristic’. Proc. 11th Int. Conf. on Telecommunications in Modern Satellite, Cable and Broadcasting Services (TELSIKS), Nis, Serbia, 2013, pp. 6972.
    9. 9)
      • 9. Soo-Chang, P., Chien-Cheng, T.: ‘IIR multiple notch filter design based on allpass filter’, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., 1997, 44, (2), pp. 133136.
    10. 10)
      • 10. Thamrongas, A., Charoenlarpnopparut, C., Prempree, P.: ‘A novel design of IIR multiple notch filter based on an all-pass filter by using a pole-reposition technique’, Sci. Asia, 2014, 40, pp. 362370.
    11. 11)
      • 11. Wang, Q., Kundur, D.: ‘A generalized design framework for IIR digital multiple notch filters’, EURASIP J. Adv. Signal Process., 2015, 2015, (26), p. 1.
    12. 12)
      • 12. Wang, Q., Yuan, H.W.: ‘Improved approach for digital multiple notch filter design’, J. Beijing Univ. Aeronaut. Astronaut., 2011, 37, (10), pp. 12501255.
    13. 13)
      • 13. Powel, M.J.D.: ‘Approximation theory and methods’ (Cambridge University Press, New York, 1981).

Related content

This is a required field
Please enter a valid email address