Abstract
A method for design of linear phase notch IIR filters is presented in this paper. The filter is realized in the form of a parallel connection of two all-pass sub-filters. In order to achieve the resulting filter with an approximately linear phase in the pass-band, the applied all-pass sub-filters should be also with a linear phase. The desired amplitude characteristic of a resulting filter is obtained by all-pass sub-filter phase approximation. It can be achieved by applying either a pure delay or an IIR all-pass filter in one branch. If a pure delay is positioned in one branch, equiripple phase of all-pass sub-filter from the other branch is guaranteed for an equiripple amplitude characteristic of the resulting filter. Efficiency of the proposed algorithm is demonstrated on a few examples. The algorithm exhibits a fast convergence and an easy determination of initial values. In the case where IIR all-pass sub-filters are placed in both branches, the resulting amplitude characteristic satisfies all the prescribed demands, but the amplitude characteristic is not equiripple even when both all-pass sub-filters have equiripple phase.
Similar content being viewed by others
References
T. Chien-Cheng, P. Soo-Chang, Stable IIR notch filter design with optimal pole placement. IEEE Trans. Signal Process. 49, 2673–2681 (2001)
M. Djurić, G. Stančić, Selective digital filters with linear phase. AEÜ Int. J. Electron. Commun. 56, 131–134 (2002)
S.K. Mitra, in Digital Signal Processing: A Computer Based Approach, 3rd edn. (McGraw Hill, New York, 2006), pp. 435–436
J.G. Proakis, D.G. Manolakis, Digital Signal Processing Principle, Algorithms, and Applications (Prentice Hall, New York, 1996), pp. 339–341
S.C.D. Roy, S.B. Jain, B. Kumar, Design of digital FIR notch filters. Proc. Inst. Electr. Eng., Vis. Image Signal Process. 141, 334–338 (1994)
T. Saramaki, On the design of digital filters as a sum of two all-pass filters. IEEE Trans. Circuits Syst. 32, 1191–1193 (1985)
G. Stančić, S. Nikolić, Design of narrow stop band recursive digital filter. Facta Univ., Electron. Energ., 16, 121–132, 2011
Y. Tian-Hu, S.K. Mitra, H. Babic, Design of linear phase FIR notch filters. Sadhana 15, 133–155 (1990)
P.P. Vaidyanathan, S.K. Mitra, Y. Neuvo, A new approach to the realization of low sensitivity IIR digital filters, IEEE Trans. Acoust. Speech Signal Process., 34, 350–361, 1986
S. Yimman, W. Hinjit, S. Sriboonsong, M. Puangpool, K. Dejhan, IIR notch filter design with modified pole-zero placements algorithm, in IEEE International Symposium on Signal Processing and Information Technology (2003), pp. 822–825
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nikolić, S., Stančić, G. Design of IIR Notch Filter with Approximately Linear Phase. Circuits Syst Signal Process 31, 2119–2131 (2012). https://doi.org/10.1007/s00034-012-9426-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-012-9426-x