Design of Multiplier-free State-Space Digital Filters

Authors: Tamal Bose, Zhurun Zhang, Miloje Radenkovic, Ojas Chauhan

Abstract:

In this paper, a novel approach is presented for designing multiplier-free state-space digital filters. The multiplier-free design is obtained by finding power-of-2 coefficients and also quantizing the state variables to power-of-2 numbers. Expressions for the noise variance are derived for the quantized state vector and the output of the filter. A “structuretransformation matrix" is incorporated in these expressions. It is shown that quantization effects can be minimized by properly designing the structure-transformation matrix. Simulation results are very promising and illustrate the design algorithm.

Keywords: Digital filters, minimum noise, multiplier-free, quantization, state-space.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1073659

References:

1] Y. Lim and S. C. Parker, "FIR filter design over a discrete powers-of-two coefficient space," IEEE Trans. Acoust., Speech, Signal Processing, vol. 31, no. 3, pp. 583-591, June 1983.
[2] Y. C. Lim and B. Liu, "The design of cascade form FIR filters for discrete space implementaion," IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, no. 7, pp. 1735-1739, Nov. 1988.
[3] H. Samueli, "An improved search algorithm for the design of multiplierless FIR filters with powers-of-two coefficients," vol. 36, no. 7, pp. 1044-1047, July 1989.
[4] S. P. Ghanekar, S. Tantaratana, and L. E. Franks, "A class of high-precision multiplier-free FIR filter realizations with periodically time-varying coefficients," IEEE Trans. Signal Processing, vol. 43, no. 4, pp. 822-830, Apr. 1995.
[5] ÔÇöÔÇö, "Design and architecture of multiplier-free FIR filter using periodically time-varying ternary coefficients," vol. 40, no. 5, pp. 364-370, May 1993.
[6] L. D. Milic and M. D. Lutovac, "Design of multiplierless elliptic IIR filters with a small quantization error," IEEE Trans. Signal Processing, vol. 47, no. 2, pp. 469-479, Feb. 1999.
[7] M. D. Lutovac and L. D. Milic, "Design of computationally efficient elliptic IIR filters with a reduced number of shift-andadd operations and multipliers," IEEE Trans. Signal Processing, vol. 45, pp. 2242-2430, Oct. 1997.
[8] L. Milic and M. D. Lutovac, "Design of multiplierless IIR filters," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., ICASSP, Munich, Germany, Apr. 1997, pp. 2201-2204.
[9] F. L. Kitson and L. Griffiths, "Design and analysis of recursive periodically time-varying digital filters with highly quantized coefficients," IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, no. 5, pp. 647-685, May 1988.
[10] S. P. Ghanekar, S. Tantaratana, and L. E. Franks, "Multiplier-free IIR filter realization using periodically time-varying state-space structureÔÇöPart I: Structure and design," IEEE Trans. Signal Processing, vol. 42, no. 5, pp. 1008-1017, May 1994.