Dejan Dragan Mirković, Miona Andrejević Stošović, Predrag Petković, Vančo Litovski

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A case study is reported related to the design of IIR digital filters exhibiting critical monotonic amplitude characteristic (CMAC) in the pass band. This kind of amplitude characteristic offers several advantages as compared to its non-monotonic counterparts while it is not studied thoroughly, if at all. After giving a short overview of the way of generation CMACs, arguments will be listed in favor of the IIR version of the digital filter function realization. Next, the IIR implementation of the digital filters will be shortly considered. The main part of the paper will be devoted to the design sequence of this kind of filters which will be illustrated on the example of a band-pass filter obtained by a set of transformations from an all-pole low-pass analogue prototype. This will be for the first time a CMAC band pass IIR digital filters to be reported.


Digital filters, IIR, monotone amplitude characteristic, all-pole filters

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D. Topisirović, V. Litovski, and M. Andrejević Stošović, “Unified theory and state-variable implementation of critical-monotonic all-pole filters,” International Journal of Circuit Theory and Applications, vol. 43, no. 4, pp. 502–515, 2015.

JF. Kaiser, Digital filters, in: FF. Kuo, JF. Kaiser (Eds.) System Analysis by Digital Computer. Wiley: New York, 1996, Chapter 7, p. 245.

D. Mirković, M. Andrejević Stošović, P. Petković and V. Litovski, “IIR digital filters with critical monotonic pass-band amplitude characteristic,” AEU - International Journal of Electronics and Communications, vol. 69, no. 10, pp. 1495-1505, Oct. 2015, ISSN 1434-8411.

DS. Humpherys, The Analysis, Design, and Synthesis of Electrical Filters, Prentice-Hall, 1970

K. Geher, Theory of Network Tolerances, Akademiai Kiadó: Budapest, Hungary, 1971.

V. Litovski, “Synthesis of monotonic passband sharp cutoff filters with constant group delay response,” Circuits and Systems, IEEE Transactions on, vol. 26, no. 8, pp. 597–602, Aug 1979.

Rabey J. Low power design essentials. Springer Science + Business Media, LLC: New York, 2009.

MF. Quélhas, A. Petraglia, MR. Petraglia, “Efficient group delay equalization of discrete-time IIR filters,” In Proceedings of the XII European Signal Processing Conference, EUSIPCO-2004, vol. 1, Vienna, Austria, 2004, pp. 125-128.

Rabrenović D, Jovanović V. Low-pass filters with critical monotonic magnitude. Publications of Faculty of Electrical Engineering, ETA series: Belgrade, 1973, pp. 59–68.

B. D. Rakovich, “Designing monotonic low-pass filters – comparison of some methods and criteria,” International Journal of Circuit Theory and Applications, vol. 2, no. 3, pp. 215–221, 1974.

S. Butterworth, “On the Theory of Filter Amplifiers,” Experimental Wireless and the Wireless Engineer, vol. 7, 1930, pp. 536-541.

A. Papoulis, “Optimum filters with monotonic response,” In Proceedings of the IRE, vol. 46, no. 3, pp. 606–609, 1958.

A. Papoulis, “On monotonic response filters,” Proceedings of the IRE, vol. 47, pp. 332–333, 1959.

M. Fukada, “Optimum filters of even orders with monotonic response,” Circuit Theory, IRE Transactions on, vol. 6, no. 3, pp. 277–281, 1959.

P. Halpern, “Optimum monotonic low-pass filters,” Circuit Theory, IEEE Transactions on, vol. 16, no. 2, pp. 240–242, May 1969.

B. Rakovich and V. Litovski, “Least-squares monotonic lowpass filters with sharp cutoff,” Electronics Letters, vol. 9, no. 4, pp. 75–76, February 1973.

D. Mirković, P. Petković, and V. Litovski, “A second order s-to-z transform and its implementation to IIR filter design,” COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 33, no. 5, pp. 1831–1843, 2014.

W. Park, K.-S. Park, and H.-M. Koh, “Active control of large structures using a bilinear pole-shifting transform with H∞ control method,” Engineering Structures, vol. 30, no. 11, pp. 3336–3344, 2008.

H. Orchard and G. C. Temes, “Filter design using transformed variables,” Circuit Theory, IEEE Transactions on, vol. 15, no. 4, pp. 385–408, 1968.

P. Geffe, “Designers guide to active bandpass filters,” Part III’, EDN, vol. 19, no. 7, 1974.

K. K. Parhi, Scaling and Round-off Noise in: VLSI digital signal processing systems: design and implementation. John Wiley & Sons, 2007, Chapter 11.

K. Prasad and P. Sathyanarayana, “Signal scaling in cascade digital filters,” Circuits, Systems and Signal Processing, vol. 8, no. 4, pp. 421–426, 1989.


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