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Optimal design of 2-D FIR digital differentiator using \(L_1\)-norm based cuckoo-search algorithm

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Abstract

In this article, an optimal design of two-dimensional finite impulse response digital differentiators (2-D FIR-DD) with quadrantally odd symmetric impulse response is presented. The design problem of 2-D FIR-DD is formulated as an optimization problem based on the \(L_1\)-error fitness function. The novel error fitness function is based on the \(L_1\) norm which is unique and is liable to produce a flat response. This design methodology incorporates advantages of \(L_1\)-error approximating function and cuckoo-search algorithm (CSA) which is capable of attaining a global optimal solution. The optimized system coefficients are computed using \(L_1\)-CSA and performance is measured in terms of magnitude response, phase response, absolute magnitude error and elapsed time. Simulation results have been compared with other optimization algorithms such as real-coded genetic algorithm and particle swarm optimization and it is observed that \(L_1\)-CSA delivers optimal results for 2-D FIR-DD design problem. Further, performance of the \(L_1\)-CSA based 2-D FIR-DD design is evaluated in terms of absolute magnitude error and algorithm execution time to demonstrate their effect with variation in the control parameters of CSA.

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References

  • Aggarwal, A., Kumar, M., Rawat, T. K., & Upadhyay, D. K. (2016a). Optimal design of 2D FIR filters with quadrantally symmetric properties using fractional derivative constraints. Circuits, Systems, and Signal Processing, 35(6), 2213–2257.

    Article  MATH  Google Scholar 

  • Aggarwal, A., Rawat, T. K., Kumar, M., & Upadhyay, D. K. (2016b). Design of optimal band-stop FIR filter using \(L_1\)-norm based RCGA. Ain Shams Engineering Journal. doi:10.1016/j.asej.2015.11.022.

  • Aggarwal, A., Rawat, T. K., Kumar, M., & Upadhyay, D. K. (2015). Optimal design of FIR high pass filter based on \(L_1\) error approximation using real coded genetic algorithm. Enggineeing Science and Technology, An International Journal, 18(4), 594–602.

    Article  Google Scholar 

  • Aggarwal, A., Rawat, T. K., & Upadhyay, D. K. (2016c). Design of optimal digital FIR filters using evolutionary and swarm optimization techniques. AEU-International Journal of Electronics and Communications, 70, 373–385.

    Article  Google Scholar 

  • Al-Alaoui, M. A. (2011). Class of digital integrators and differentiators. IET Signal Processing, 5(2), 251–260.

    Article  Google Scholar 

  • Bhattacharya, D., & Antoniou, A. (1999). Design of 2-D FIR filters by a feedback neural network. Multidimensional Systems and Signal Processing, 10(3), 319–330.

    Article  MATH  Google Scholar 

  • Chu, C. H., Delp, E. J., & Buda, A. J. (1988). Detecting left ventricular endocardial and epicardial boundaries by digital two-dimensional echocardiography. IEEE Transactions on Medical Imaging, 7(2), 81–90.

    Article  Google Scholar 

  • Cichocki, A., & Amari, S. I. (2002). Adaptive blind signal and image processing: Learning algorithms and applications (Vol. 1). Hoboken: Wiley.

    Book  Google Scholar 

  • Dhabal, S., & Venkateswaran, P. (2015). A novel accelerated artificial bee colony algorithm for optimal design of two dimensional FIR filter. Multidimensional Systems and Signal Processing. doi:10.1007/s11045-015-0352-5

  • Gandomi, A. H., Yang, X. S., & Alavi, A. H. (2013). Cuckoo search algorithm: A metaheuristic approach to solve structural optimization problems. Engineering with Computers, 29(1), 17–35.

    Article  Google Scholar 

  • Grossmann, L. D., & Eldar, Y. C. (2007). An \(L_1\)-method for the design of linear-phase FIR digital filters. IEEE Transactions on Signal Processing, 55(11), 5253–5266.

    Article  MathSciNet  Google Scholar 

  • Gupta, M., Jain, M., & Kumar, B. (2011). Recursive wideband digital integrator and differentiator. International Journal of Circuit Theory and Applications, 39, 775–782.

    Article  Google Scholar 

  • Gupta, M., Relan, B., Yadav, R., & Aggarwal, V. (2014). Wideband digital integrators and differentiators designed using particle swarm optimization. IET Signal Processing, 8(6), 668–679.

    Article  Google Scholar 

  • Gupta, M., & Yadav, R. (2014). New improved fractional order differentiator models based on optimized digital differentiators. The Scientific World Journal. doi:10.1155/2014/741395.

  • Hinamoto, T., & Doi, A. (1996). A technique for the design of 2-D recursive digital filters with guaranteed stability. Multidimensional Systems and Signal Processing, 7(2), 225–237.

    Article  MATH  Google Scholar 

  • Jalloul, M. K., & Al-Alaoui, M. A. (2015). Design of recursive digital integrators and differentiators using particle swarm optimization. International Journal of Circuit Theory and Applications. doi:10.1002/cta.2115.

  • Kockanat, S., & Karaboga, N. (2015). The design approaches of two-dimensional digital filters based on meta-heuristic optimization algorithms: A review of the literature. Artificial Intelligence Review, 44(2), 265–287.

  • Kumar, M., & Rawat, T. K. (2015a). Optimal design of FIR fractional order differentiator using cuckoo search algorithm. Expert Systems with Applications, 42, 3433–3449.

    Article  Google Scholar 

  • Kumar, M., & Rawat, T. K. (2015b). Optimal fractional delay-IIR filter design using cuckoo search algorithm. ISA Transactions, 59, 39–54.

    Article  Google Scholar 

  • Kumar, M., Rawat, T. K., Jain, A., Singh, A. A., & Mittal, A. (2015a). Design of digital differentiators using interior search algorithm. Procedia Computer Science, 57, 368–376.

    Article  Google Scholar 

  • Kumar, M., Rawat, T. K., Singh, A. A., Mittal, A., Jain, A. (2015b). Optimal design of wideband digital integrators using gravitational search algorithm. In International conference on international conference on computing, communication and automation (ICCCA), pp. 1314–1319.

  • Lai, X. (2007). Design of smallest size two-dimensional linear-phase FIR filters with magnitude error constraint. Multidimensional Systems and Signal Processing, 18(4), 341–349.

    Article  MATH  Google Scholar 

  • Lee, J. S. (1980). Digital image enhancement and noise filtering by use of local statistics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2, 165–168.

    Article  Google Scholar 

  • Lin, Y. P., & Vaidyanathan, P. P. (1996). Theory and design of two-dimensional filter banks: A review. Multidimensional Systems and Signal Processing, 7(3–4), 263–330.

    Article  MATH  Google Scholar 

  • Lu, W. S., & Hinamoto, T. (2011). Two-dimensional digital filters with sparse coefficients. Multidimensional Systems and Signal Processing, 22(1–3), 173–189.

    Article  MathSciNet  MATH  Google Scholar 

  • Pan, B., Xie, H., Guo, Z., & Hua, T. (2007). Full-field strain measurement using a two-dimensional Savitzky–Golay digital differentiator in digital image correlation. Optical Engineering, 46(3), 033601–033601.

    Article  Google Scholar 

  • Patwardhan, A. P., Patidar, R., & George, N. V. (2014). On a cuckoo search optimization approach towards feedback system identification. Digital Signal Processing, 32, 156–163.

    Article  Google Scholar 

  • Rawat, T. K. (2015). Digital signal processing (1st ed.). New Delhi: Oxford Publication.

    Google Scholar 

  • Shyu, J. J., Pei, S. C., Huang, Y. D., & Chen, Y. S. (2014). A new structure and design method for variable fractional-delay 2-D FIR digital filters. Multidimensional Systems and Signal Processing, 25(3), 511–529.

    Article  Google Scholar 

  • Tseng, C. C., & Lee, S. L. (2008). Design of digital differentiator using difference formula and richardson extrapolation. IET Signal Processing, 2(2), 177–188.

    Article  MathSciNet  Google Scholar 

  • Tseng, C. C., & Lee, S. L. (2013). Designs of two-dimensional linear phase FIR filters using fractional derivative constraints. Signal Processing, 93(5), 1141–1151.

    Article  Google Scholar 

  • Tseng, C. C., & Lee, S. L. (2014). Designs of fractional derivative constrained 1-D and 2-D FIR filters in the complex domain. Signal Processing, 95, 111–125.

    Article  Google Scholar 

  • Tzafestas, S. G. (1986). Multidimensional systems, techniques and applications. New York: Marcel Dekker.

    MATH  Google Scholar 

  • Tzeng, S. T. (2004). Genetic algorithm approach for designing 2-D FIR digital filters with 2-D symmetric properties. Signal Processing, 84(10), 1883–1893.

    Article  MATH  Google Scholar 

  • Upadhyay, D. K., & Singh, R. K. (2011). Recursive wide band digital differentiators and integrators. Electronic Letters, 47(11), 647648.

    Article  Google Scholar 

  • Yang, X. S. (2014). Nature-inspired optimization algorithms. Amsterdam: Elsevier.

    MATH  Google Scholar 

  • Yang, X. S., Cui, Z., Xiao, R., Gandomi, A. H., & Karamanoglu, M. (2013). Swarm intelligence and bio-inspired computation: Theory and applications (1st ed.). Amsterdam: Elsevier.

    Google Scholar 

  • Yang, X. S., Deb, S. (2009). Cuckoo search via lvy flights. In Proceeding of world congress on nature and biologically inspired computing, IEEE Publications, pp. 210–214.

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Authors and Affiliations

  1. Department of Electronics and Communication, Netaji Subhas Institute of Technology, Delhi, India

    Apoorva Aggarwal, Manjeet Kumar, Tarun K. Rawat & D. K. Upadhyay

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  1. Apoorva Aggarwal
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  2. Manjeet Kumar
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  3. Tarun K. Rawat
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  4. D. K. Upadhyay
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Correspondence to Manjeet Kumar.

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Aggarwal, A., Kumar, M., Rawat, T.K. et al. Optimal design of 2-D FIR digital differentiator using \(L_1\)-norm based cuckoo-search algorithm. Multidim Syst Sign Process 28, 1569–1587 (2017). https://doi.org/10.1007/s11045-016-0433-0

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  • DOI: https://doi.org/10.1007/s11045-016-0433-0

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