{"title":"广义边际时频分布","authors":"X. Xia, Y. Owechko, B. Soffer, R. Matic","doi":"10.1109/TFSA.1996.550104","DOIUrl":null,"url":null,"abstract":"We introduce a family of time-frequency (TF) distributions with generalized-marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitude squared of the fractional Fourier transforms of the signal. We present a necessary and sufficient condition for a TF distribution in the Cohen's class to satisfy generalized-marginals. We then modify the existing well-known TF distributions in the Cohen's class, such as Choi-Williams, Page distributions, so that the modified ones have generalized marginals. Numerical examples are presented to show that the proposed TF distributions have the advantages of both Wigner-Ville and other quadratic TF distributions which only have the conventional marginals. Moreover, they also indicate that the generalized-marginal TF distributions with proper marginals are more robust than the Wigner-Ville and the Choi-Williams distributions when signals contain additive noise.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Generalized-marginal time-frequency distributions\",\"authors\":\"X. Xia, Y. Owechko, B. Soffer, R. Matic\",\"doi\":\"10.1109/TFSA.1996.550104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a family of time-frequency (TF) distributions with generalized-marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitude squared of the fractional Fourier transforms of the signal. We present a necessary and sufficient condition for a TF distribution in the Cohen's class to satisfy generalized-marginals. We then modify the existing well-known TF distributions in the Cohen's class, such as Choi-Williams, Page distributions, so that the modified ones have generalized marginals. Numerical examples are presented to show that the proposed TF distributions have the advantages of both Wigner-Ville and other quadratic TF distributions which only have the conventional marginals. Moreover, they also indicate that the generalized-marginal TF distributions with proper marginals are more robust than the Wigner-Ville and the Choi-Williams distributions when signals contain additive noise.\",\"PeriodicalId\":415923,\"journal\":{\"name\":\"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)\",\"volume\":\"57 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1996-06-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/TFSA.1996.550104\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TFSA.1996.550104","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce a family of time-frequency (TF) distributions with generalized-marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitude squared of the fractional Fourier transforms of the signal. We present a necessary and sufficient condition for a TF distribution in the Cohen's class to satisfy generalized-marginals. We then modify the existing well-known TF distributions in the Cohen's class, such as Choi-Williams, Page distributions, so that the modified ones have generalized marginals. Numerical examples are presented to show that the proposed TF distributions have the advantages of both Wigner-Ville and other quadratic TF distributions which only have the conventional marginals. Moreover, they also indicate that the generalized-marginal TF distributions with proper marginals are more robust than the Wigner-Ville and the Choi-Williams distributions when signals contain additive noise.