In this paper, we present a novel and efficient method for the design of a sharp, two dimensional (2D) wideband, circularly symmetric, FIR filter. First of all, a sharp one dimensional (1D) infinite precision FIR filter is designed using the Frequency Response Masking (FRM) technique. This filter is converted into a multiplier-less filter by representing it in the Canonic Signed Digit (CSD) space. The design of the FRM filter in the CSD space calls for the use of a discrete optimization technique. To this end, a new optimization approach is proposed using a modified Harmony Search Algorithm (HSA). HSA is modified in such a way that, in every exploitation and exploration phase, the candidate solutions turns out to be integers. The 1D FRM multiplier-less filter, is in turn transformed to the 2D equivalent using the recently proposed multiplier-less transformations namely, T1 and T2. These transformations are successful in generating circular contours even for wideband filters. Since multipliers are the most power consuming elements in a 2D filter, the multiplier-less realization calls for reduced power consumption as well as computation time. Significant reduction in the computational complexity and computation time are the highlights of our proposed design technique. Besides, the proposed discrete optimization using modified HSA can be used to solve optimization problems in other engineering disciplines, where the search space consists of integers.
Y. C. Lim, “Frequency Response Masking Approach for the Synthesis of Sharp Linear Phase Digital Filters,” IEEE Transactions on Circuits and Systems, Vol. 33, No. 4, 1986, pp. 357-364. doi:10.1109/TCS.1986.1085930
Y. C. Lim, Y. J. Yu, K. L. Teo and T. Saramaki, “FRM- Based FIR Filters with Optimum Finite Word-Length Performance,” IEEE Transactions on Signal Processing, Vol. 55, No. 6, 2007, pp. 2914-2924.
Y. J. Yu and Y. C. Lim, “Genetic Algorithm Approach for the Optimization of Multiplierless Sub-Filters Generated by the Frequency Response Masking Technique,” Proceedings of IEEE International Conference on Electronics, Circuits and Systems, Vol. 3, Croatia, 2002, pp. 1163-1166.
R. I. Hartley, “Subexpression Sharing in Filters Using Canonic Signed Digit Multipliers,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 43, No. 10, 1996, pp. 677-688.
B. Elkarami and M. Ahmadi, “An Efficient Design of 2-D FIR Digital Filters by Using Singular Value Decomposition and Genetic Algorithm with Canonical Signed Digit (CSD) Coefficients,” Proceedings of Midwest Symposium on Circuits and Systems, Seoul, 7-10 August 2011, pp. 1- 4.
P. Mercier, S. Mohan-Kilambi and B. Nowrouzian, “Optimization of FRM FIR Digital Filters over CSD and DBNS Multiplier Coefficient Spaces Employing a Novel Genetic Algorithm,” Computers, Vol. 2, No. 7, 2007, pp. 20-31.
J. C. Liu and Y. L. Tai, “Design of 2-DWideband Circularly Symmetric FIR Filters by Multiplier-Less High- Order Transformation,” IEEE Transactions on Circuits Systems I, Vol. 58, No. 4, 2011, pp. 746-754.
E. M. Kermani, H. Salehinejad and S. Talebi, “PAPR Reduction of OFDM Signals Using Harmony Search Algorithm,” Proceedings of International Conference on Telecommunications, Cyprus, 8-11 May 2011, pp. 90-94.
R. M. Mersereau, W. F. G. Mecklenbrauker and T. F. Quatieri, Jr., “McClellan Transformations for Two-Di- mensional Digital Filtering: I Design,” IEEE Transactions on Circuits Systems, Vol. 23, No. 7, 1976, pp. 405- 414. doi:10.1109/TCS.1976.1084236
W. S. Lu and T. Hinamoto, “Optimal Design of Frequency-Response-Masking Filters Using Semidefinite Programming,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 50, No. 4, 2003, pp. 557-568.
M. Manuel and E. Elias, “Design of Frequency Response Masking FIR Filter in the Canonic Signed Digit Space Using Modified Artificial Bee Colony Algorithm,” Engineering Applications of Artificial Intelligence, 2012, In Press. doi:10.1016/j.engappai.2012.02.010
Y. C. Lim, R. Yang, D. N. Li and J. J. Song, “Signed Power-of-Two Term Allocation Scheme for the Design of Digital Filters,” IEEE Transactions on Circuits and Systems II, Vol. 46, No. 5, 1999, pp. 577-584.
K. Lee and Z. Geem, “A New Meta-Heuristic Algorithm for Continuous Engineering Optimization: Harmony Search Theory and Practice,” Computer Methods in Applied Mechanics and Engineering, Vol. 194, No. 36-38, 2005, pp. 3902-3933. doi:10.1016/j.cma.2004.09.007