The Journal of the Institute of Internet, Broadcasting and Communication (한국인터넷방송통신학회논문지)

The Institute of Internet, Broadcasting and Communication (한국인터넷방송통신학회)
권호 표지
DOI QR코드

DOI QR Code

Wiener-Hopf Equation with Robustness to Application System

응용시스템에 강건한 Wiener-Hopf 방정식

  • 조주필 (군산대학교 전파공학과) ;
  • 이일규 (공주대학교 전기전자제어공학부) ;
  • 차재상 (서울과학기술대학교 매체공학과)
  • Received : 2011.07.12
  • Accepted : 2011.08.12
  • Published : 2011.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equivalent to original Wiener-Hopf equation. In conclusion, our method can find the coefficient of the TDL (tapped-delay-line) filter where a lattice filter is used, and also when the process of Gram-Schmidt orthogonalization is used. Furthermore, a new cost function is suggested which may facilitate research in the adaptive signal processing area.

본 논문에서 등가의 Wiener-Hopf 공식을 제안한다. 제안된 알고리듬은 입력신호들이 직교하는 경우 TDL 필터의 가중치 벡터와 오차를 동시에 가질 수 있게 된다. 등가의 Wiener-Hopf 방정식은 최소 평균 자승 오차 방식에 근여 이론적으로 분석이 되었다. 제안된 알고리듬의 성능 결과는 원래 Wiener-Hopf 방정식의 성능과 동일함을 확인할 수 있다. 결론적으로 제안된 방식은 격자 필터가 적용되는 경우 TDL 필터 계수를 가지게 된다. 게다가 새로운 비용함수가 제안되어 더욱 우수한 적응신호처리 분야에서의 발전을 보일 것으로 기대된다.

Keywords

References

  1. Haykin, Adaptive Filter Theory-Fourth Edition, PrenticeHall.
  2. J. G. Proakis, C. M. Rader, F. Ling and C. L. Nikias, Advanced Digital Signal Processing. Macmillan Publishing Company,1992.
  3. P. S. R. Diniz, Adaptive Filtering -Algorithms and Practical Implementation, second edition. Kluwer Academic Publishers, 2002.
  4. J. Makhoul. "A Class of ALL-Zero Lattice Digital Filters: Properties" IEEE Trans. Acoustics, Speech, and Signal Processing, vol. ASSP-26, pp.304-314, Aug. 1978.
  5. E. Karlsson, M. Hayes, "Least squares ARMA modeling of linear time-varying systems: Lattice filter structures and fast RLS algorithms," IEEE Trans. Acoustics, Speech, and Signal Processing, vol.ASSP-35, NO.7, pp.994-1014, July1987.
  6. H. K. Baik, V. J. Mathews, "Adaptive lattice bilinear filters," IEEE Trans. on Signal Processing, vol.41, pp.2033-2046, June1993. https://doi.org/10.1109/78.218134
  7. L. Fuyun, J. Proakis, "A generalized multichannel least squares lattice algorithm based on sequential processing stages," IEEE Trans. on Signal Processing, vol.32, pp.381-389, Apr.1984. https://doi.org/10.1109/TASSP.1984.1164325