Cumulant Based Wiener Filtering

• Main Authors: Chih-Chun Feng, 馮治軍
• Other Authors: Chong-Yung Chi; Wen-Rong Wu
• Format: Others
• Language: en_US
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/15833242750076017911

碩士 === 國立交通大學 === 電信研究所 === 82 === This thesis proposes a cumulant (higher-order statistics) based mean-square-error (MSE) criterion for the design of Wiener filters when both the given wide-sense stationary random signal x(n) and the desired signal d(n) are non-Gaussian and contami- nated by Gaussian noise sources. It is shown that the designed cumulant based Wiener filter associated with the proposed cri- terion is identical to the conventional correlation (second- order statistics) based Wiener filter as if both x(n) and d(n) were noise-free measurements. As the latter, the former can be also obtained by solving a cumulant based Wiener-Hopf equation associated with a (cumulant based) orthogonality principle. Then a generalized cumulant based projection theorem is proposed which includes the projection of cumulants to correlations as- sociated with the proposed cumulant based MSE criterion and that associated with Delopoulos and Giannakis' cumulant based MSE criterion as special cases. Moreover, the proposed cumulant based criterion and Delopoulos and Giannakis' cumulant based MSE criterion are equivalent for cumulant order M = 3. The proposed cumulant based Wiener filter is then applied to time delay esti- mation and system identification. Some simulation results are then provided to demonstrate the good performance of the pro- posed cumulant based Wiener filter. Finally, we draw some con- clusions.