An Algorithm Proposed for FIR Filter Coefficients Representation

Authors: Mohamed Al Mahdi Eshtawie, Masuri Bin Othman

Abstract:

Finite impulse response (FIR) filters have the advantage of linear phase, guaranteed stability, fewer finite precision errors, and efficient implementation. In contrast, they have a major disadvantage of high order need (more coefficients) than IIR counterpart with comparable performance. The high order demand imposes more hardware requirements, arithmetic operations, area usage, and power consumption when designing and fabricating the filter. Therefore, minimizing or reducing these parameters, is a major goal or target in digital filter design task. This paper presents an algorithm proposed for modifying values and the number of non-zero coefficients used to represent the FIR digital pulse shaping filter response. With this algorithm, the FIR filter frequency and phase response can be represented with a minimum number of non-zero coefficients. Therefore, reducing the arithmetic complexity needed to get the filter output. Consequently, the system characteristic i.e. power consumption, area usage, and processing time are also reduced. The proposed algorithm is more powerful when integrated with multiplierless algorithms such as distributed arithmetic (DA) in designing high order digital FIR filters. Here the DA usage eliminates the need for multipliers when implementing the multiply and accumulate unit (MAC) and the proposed algorithm will reduce the number of adders and addition operations needed through the minimization of the non-zero values coefficients to get the filter output.

Keywords: Pulse shaping Filter, Distributed Arithmetic, Optimization algorithm.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060032

References:

[1] Mariusz Rawski, Pawel Tomaszewicz, Henry Selvaraj, and Tadeusz Luba, ''Efficient Implementation of Digital Filters with Use of Advanced Synthesis Methods Targeted FPGA Architectures'', 8th Euromicro conference on digital system design (DSD'05), IEEE Computer Society, 2005.
[2] P. Lapsley, J. Bier, A. Shoham, and E. Lee, ''DSP Processor Fundamentals'', IEEE Press, New york 1997. E. Lee, ''Programmable DSP Architectures: PartI'', IEEE Transactions on Acoustics, Speech and Signal Processing Magazine, 1988, pp. 4-19.
[3] E. Lee, ''Programmable DSP Architectures: PartII'', IEEE Transactions on Acoustics, Speech and Signal Processing Magazine, 1989, pp. 4-14.
[4] Dongsong Zeng, Annamalai Annamalai Jr., Amir I. Zaghloul, ''Pulse-shaping filter design in UWB system,'' IEEE conference on Ultra Wideband Systems and Technology, Reston, Virginia, Nov, 16-19, 2003, pp. 66-70.
[5] S Herman, "The complete ghost canceler," ICCE'93 Educational session, June 1993. D. Suckley, "Genetic algorithm in the design of FIR filters," Inst. Elect. Eng. Proc., vol. 138, pt. G. pp. 234-238, 1991. Stanley A. White, "Applications of distributed arithmetic to digital signal processing: A tutorial review," IEEE ASSP magazine July, 1989.
[6] J. R. Choi, L.H. Jang, S. W. Jung, and J. H Choi, "Structured design of a 288-tap FIR filter by optimized partial product tree compression," IEEE J. Solid-State Circuits, vol. 32, pp. 468-476, Mar. 1997.
[7] T. W. Parksand J. H. McClellan, "A program for the design of linear phase finite impulse response digital filters," IEEE Trans. Audio Electroacoust., vol. AU-20, pp.195-199, 1972.
[8] C. J. Nicol, P. Larsson, K. Azadet, and J. H. O'Neill, "A low-power 128-tap digital adaptive equalizer for broadband modems," IEEE J. Solid-State Circuits, vol. 32 pp. 1777-1789, Nov. 1997.
[9] Kyung-Saeng Kim and Kwyro Lee, "Low-power and area efficient FIR filter implementation suitable for multiple tape," IEEE Trans. On VLSI systems, vol. 11, No. 1, Feb. 2003.
[10] Tang Zhangwen, Zahang Zahnpeng, Zhang Jie, and Min Hao, ''A High-Speed, Programmable, CSD Coefficient FIR filter'', ICASSP
[11] Mohamed A. Eshtawie and Masuri Othman," On-Line DA-LUT Architecture for High-Speed High-Order Digital FIR Filters," paper status is published in the tenth IEEE international conference on communication systems (IEEE ICCS 2006), 30-1 Nov. 2006 Singapore.
[12] Shimon Moshavi, "Multi-user detection fo DS-CDMA communications," IEEE Communication Magazine, October 1996.
[13] Jhone G. Proakis, Masoud Salehi, and Gerhard Bauch, Contemporary Communication Systems using MATLAB. Brooks/Cole, 2004.