Design of optimal 2-D FIR differentiators with quadrantally symmetric properties using the L1-method

In this paper the design of 2-dimensional finite impulse response (2-D FIR) digital differentiator (DD) with quadrantally odd symmetric impulse response is presented. The L1-method is developed to design the 2-D system and minimize the L1-error. The design problem of 2-D FIR-DD is formulated as an optimization problem in order to compute the system coefficients with quadrantally odd symmetric properties. Finally, the design examples of 2-D differentiator of different order is demonstrated and analyzed in terms of the L1-error and elapsed time. The proposed 2-D FIR L1-DD is also compared with the existing 2-D differentiators designed using metaheuristic techniques and is observed to yield least L1-error.

[1]  Takao Hinamoto,et al.  Two-dimensional digital filters with sparse coefficients , 2011, Multidimens. Syst. Signal Process..

[2]  Naoyuki Aikawa,et al.  An L1-Approximation for the design of FIR digital filters with complex coefficients , 2015 .

[3]  Chien-Cheng Tseng,et al.  Designs of fractional derivative constrained 1-D and 2-D FIR filters in the complex domain , 2014, Signal Process..

[4]  Tarun Kumar Rawat,et al.  Optimal design of 2-D FIR digital differentiator using $$L_1$$L1-norm based cuckoo-search algorithm , 2017, Multidimens. Syst. Signal Process..

[5]  Tarun Kumar Rawat,et al.  Optimal Design of 2D FIR Filters with Quadrantally Symmetric Properties Using Fractional Derivative Constraints , 2016, Circuits Syst. Signal Process..

[6]  Tarun Kumar Rawat,et al.  Optimal design of FIR high pass filter based on L1 error approximation using real coded genetic algorithm , 2015 .

[7]  Soo-Chang Pei,et al.  A new structure and design method for variable fractional-delay 2-D FIR digital filters , 2014, Multidimens. Syst. Signal Process..

[8]  Nurhan Karaboga,et al.  The design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms: a review of the literature , 2014, Artificial Intelligence Review.

[9]  Tarun Kumar Rawat,et al.  Design of optimal band-stop FIR filter usingL1-norm based RCGA , 2016, Ain Shams Engineering Journal.

[10]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[11]  YUAN-PEl LIN,et al.  Theory and Design of Two-Dimensional Filter Banks : A Review , 2008 .

[12]  Apoorva Aggarwal,et al.  Design of Hilbert transformer using the L1-method , 2015, 2015 Annual IEEE India Conference (INDICON).

[13]  Naoyuki Aikawa,et al.  An L1-Approximation for the Design of FIR Digital Filters with Complex Coefficients , 2015 .

[14]  L. Goddard.  Approximation of Functions , 1965, Nature.

[15]  Manjeet Kumar,et al.  Efficient Design of Digital FIR Differentiator using $L_1$-Method , 2016 .

[16]  Huimin Xie,et al.  Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation , 2007 .

[17]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[18]  LeeJong-Sen.  Digital Image Enhancement and Noise Filtering by Use of Local Statistics , 1980 .

[19]  E J Delp,et al.  Detecting left ventricular endocardial and epicardial boundaries by digital two-dimensional echocardiography. , 1988, IEEE transactions on medical imaging.

[20]  Yonina C. Eldar,et al.  An $L_1$-Method for the Design of Linear-Phase FIR Digital Filters , 2007, IEEE Transactions on Signal Processing.

[21]  Spyros G. Tzafestas,et al.  Multidimensional Systems: Techniques and Applications , 1986 .

[22]  Palaniandavar Venkateswaran,et al.  A novel accelerated artificial bee colony algorithm for optimal design of two dimensional FIR filter , 2017, Multidimens. Syst. Signal Process..