Nonexistence of cross-term free time-frequency distribution with concentration of Wigner-Ville distribution  

作　　者：邹红星 卢旭光 戴琼海 李衍达 

机构地区：Department of Automation, Tsinghua University, Beijing 100084, China[1] Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China[2]

出　　处：《Science in China(Series F)》2002年第3期174-180,共7页中国科学（F辑英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 60172026);the Basic Research Foundation of Tsinghua University (Grant No. JC2001028); and the Scientific Innovation Foundation of Ph. D. Candidates of Tsinghua Uni

摘　　要：Wigner-Ville distribution (WVD) is recognized as being a powerful tool and a nucleus in time-frequency representation (TFR) which gives an excellent time-frequency concentration, and more importantly, has many desirable properties. A major shortcoming of WVD is the inherent cross-term (CT) interference. Although solutions to this problem from the bulk of contributions to the literature concerning TFR are currently available, none has been able to completely eliminate the CT’s in WVD. It is therefore a common belief that if there exists an auxiliary time-frequency distribution (TFD) which has the same auto-terms (AT’s) as that in WVD, but has CT’s with the opposite sign, then, by adding the auxiliary TFD to WVD, an ideal TFD, which preserves the concentration of WVD while annihilating the CT’s, is readily obtained. However, we prove that the auxiliary TFD does not exist. Moreover, it is found that in general, CT free joint distributions with their concentrations close to that of WVD do not exist either.Wigner-Ville distribution (WVD) is recognized as being a powerful tool and a nucleus in time-frequency representation (TFR) which gives an excellent time-frequency concentration, and more importantly, has many desirable properties. A major shortcoming of WVD is the inherent cross-term (CT) interference. Although solutions to this problem from the bulk of contributions to the literature concerning TFR are currently available, none has been able to completely eliminate the CT's in WVD. It is therefore a common belief that if there exists an auxiliary time-frequency distribution (TFD) which has the same auto-terms (AT's) as that in WVD, but has CT's with the opposite sign, then, by adding the auxiliary TFD to WVD, an ideal TFD, which preserves the concentration of WVD while annihilating the CT's, is readily obtained. However, we prove that the auxiliary TFD does not exist. Moreover, it is found that in general, CT free joint distributions with their concentrations close to that of WVD do not exist either.

关 键 词：time-frequency analysis Wigner-Ville distribution cross-term cancellation. 

分 类 号：TN911.6[电子电信—通信与信息系统]