DOI QR코드

DOI QR Code

Design of FIR Filters With Sparse Signed Digit Coefficients

희소한 부호 자리수 계수를 갖는 FIR 필터 설계

  • Kim, Seehyun (Dept. of Information and Communication Engineering, The University of Suwon)
  • Received : 2015.07.10
  • Accepted : 2015.09.02
  • Published : 2015.09.30

Abstract

High speed implementation of digital filters is required in high data rate applications such as hard-wired wide band modem and high resolution video codec. Since the critical path of the digital filter is the MAC (multiplication and accumulation) circuit, the filter coefficient with sparse non-zero bits enables high speed implementation with adders of low hardware cost. Compressive sensing has been reported to be very successful in sparse representation and sparse signal recovery. In this paper a filter design method for digital FIR filters with CSD (canonic signed digit) coefficients using compressive sensing technique is proposed. The sparse non-zero signed bits are selected in the greedy fashion while pruning the mistakenly selected digits. A few design examples show that the proposed method can be utilized for designing sparse CSD coefficient digital FIR filters approximating the desired frequency response.

광대역 통신 모뎀이나 초고해상도 비디오 코덱 등과 같이 높은 데이터율을 갖는 시스템을 하드웨어로 구현할 때에는 디지털 필터의 고속 구현이 필수적이다. 디지털 필터의 임계경로는 대부분 MAC (multiplication and accumulation) 연산 회로이므로 필터 계수의 0이 아닌 비트의 갯수가 희소하다면 하드웨어 비용이 적은 덧셈기로도 디지털 필터를 고속으로 구현할 수 있다. 압축센싱은 신호의 희소 표현이나 희소 신호의 복원에 우수한 성능을 보임이 최근 연구에서 보고되고 있다. 본 논문에서는 압축센싱에 기반한 디지털 FIR 필터의 CSD (canonic signed digit) 계수를 찾는 방법을 제안한다. 주어진 주파수 응답과의 오차를 최소하면서 탐욕적 방법으로 희소한 0이 아닌 부호자리수를 찾고 잘못 선택되었던 부호자리수는 제거하는 과정을 반복한다. 설계 예를 통해 제안된 방법으로 희소한 0이 아닌 CSD 계수의 FIR 필터를 설계할 수 있음을 보인다.

Keywords

References

  1. R. Hartley, "Optimization of canonic signed digit multipliers for filter design," Proc. IEEE International Symposium on Circuits and Systems, pp. 1992-1995, Jun., 1991.
  2. K. Hwang, Computer Arithmetic, Principles, Architecture, and Design, New York, Wiley, 1979.
  3. E. Candes, J. Romberg, and T. Tao, " Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Information Theory, vol. 52, no. 2, pp. 489-509, February, 2006. https://doi.org/10.1109/TIT.2005.862083
  4. D. Donoho, "Compressed sensing," IEEE Trans., Information Theory, vol. 52, no. 4, pp. 1289-1306, Apri, 2006. https://doi.org/10.1109/TIT.2006.871582
  5. E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Information Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. https://doi.org/10.1109/TIT.2005.858979
  6. J. A. Tropp, "Greed is good: algorithmic results for sparse approximation," IEEE Trans. Information Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004. https://doi.org/10.1109/TIT.2004.834793
  7. D. Donoho, Y. Tsaig I. Drori, and J. Starck, "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," IEEE Trans. Information Theory, vol. 58, no. 2, pp. 1094-1121, Feb. 2012. https://doi.org/10.1109/TIT.2011.2173241
  8. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmon.Anal., vol 26, no. 3, pp. 301-321, May 2009 https://doi.org/10.1016/j.acha.2008.07.002
  9. S. Kim, "Compressive sensing of the FIR filter coefficients for multiplierless implementation," J . Korea Institute of Information and Communication Engineering, vol. 18, no. 10, pp. 2375-2381 Oct., 2014 https://doi.org/10.6109/jkiice.2014.18.10.2375
  10. H. Samueli, "An improved search algorithm for the design of multiplierless FIR filters with powers-of-two coefficients," IEEE Trans. Circuits and Systems, vol. 36, no. 7, pp. 1044-1047, July, 1989. https://doi.org/10.1109/31.31347
  11. N. Takahashi and K. Suyama, "Design of CSD coefficient FIR filters based on branch and bound method," Proc. International Symposium on Communications and Information Technologgies, Oct 2010, pp. 575-578