Circuits, Systems, and Signal Processing

, Volume 38, Issue 5, pp 2187–2226 | Cite as

A New Method for Designing of Stable Digital IIR Filter Using Hybrid Method

  • N. Agrawal
  • A. KumarEmail author
  • Varun Bajaj


In this paper, a new technique for designing of a stable digital infinite impulse response filter, with improved performance in passband and stopband regions using quantum particle swarm optimization (QPSO) and artificial bee colony (ABC) algorithm, is explored in frequency domain. In the proposed method, QPSO technique is modified with exploiting the novelty of search and replacement mechanism of scout bee from ABC algorithm. For this purpose, a new design problem is constructed as a nonlinear minimization of mean square error between the designed and desired filter responses in passband, stopband, and transition band simultaneously, allowing permissible ripples in passband and stopband. Efficiency of the proposed technique is measured by several attributes like passband error, stopband error, total squared error (SE), maximum stopband attenuation, maximum passband error \( \left( {e_{pb}^{\hbox{max} } } \right) \), passband ripple, and maximum phase deviation in passband. Experimental results evidence that a significant reduction is achieved in sum of the SE in passband and stopband from 12 to 54%, and the performance is not degraded due to quantization and truncation process. However, computation time in term of CPU time is increased from 0.77 to 4.1%, along with 2.62–7.43% hike in number of function evaluation, when compared to QPSO. A comparative study reveals that the proposed method yields better fidelity parameter as compared other evolutionary algorithms such as gravitational search algorithm, genetic algorithm, and variants of PSO. The proposed technique is also suitable for higher filter taps.


Infinite impulse response (IIR) Quantum particle swarm optimization (QPSO) Particle swarm optimization (PSO) Artificial bee colony (ABC) Modified MSE Stability Lattice Quantization error 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Discipline of Electronics and Communication EngineeringPDPM Indian Institute of Information Technology, Design and Manufacturing JabalpurJabalpurIndia

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