{"title":"时频分布的计算复杂度","authors":"M. Vishwanath, R. Owens, M. Irwin","doi":"10.1109/SSAP.1992.246880","DOIUrl":null,"url":null,"abstract":"A number of lower bounds on the communication and multiplicative complexity are derived. The (Area)*(Time)/sup 2/ (AT/sup 2/) bound for the discrete short time Fourier transform, the discrete Wigner-Ville distribution, the discrete ambiguity function and the discrete Gabor transform is shown to be AT/sup 2/= Omega (N/sup 3/ log/sup 2/ N), where N/sup 2/ is the number of output points. The lower bound on multiplicative complexity for these is shown to be Omega (N/sup 2/). For the N-point discrete wavelet transform a lower bound of AT/sup 2/= Omega (N/sup 2/ log/sup 2/ N) and a multiplicative complexity of Omega (N) are the same as the lower bounds for the DFT.<<ETX>>","PeriodicalId":309407,"journal":{"name":"[1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"The computational complexity of time-frequency distributions\",\"authors\":\"M. Vishwanath, R. Owens, M. Irwin\",\"doi\":\"10.1109/SSAP.1992.246880\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A number of lower bounds on the communication and multiplicative complexity are derived. The (Area)*(Time)/sup 2/ (AT/sup 2/) bound for the discrete short time Fourier transform, the discrete Wigner-Ville distribution, the discrete ambiguity function and the discrete Gabor transform is shown to be AT/sup 2/= Omega (N/sup 3/ log/sup 2/ N), where N/sup 2/ is the number of output points. The lower bound on multiplicative complexity for these is shown to be Omega (N/sup 2/). For the N-point discrete wavelet transform a lower bound of AT/sup 2/= Omega (N/sup 2/ log/sup 2/ N) and a multiplicative complexity of Omega (N) are the same as the lower bounds for the DFT.<<ETX>>\",\"PeriodicalId\":309407,\"journal\":{\"name\":\"[1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SSAP.1992.246880\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SSAP.1992.246880","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The computational complexity of time-frequency distributions
A number of lower bounds on the communication and multiplicative complexity are derived. The (Area)*(Time)/sup 2/ (AT/sup 2/) bound for the discrete short time Fourier transform, the discrete Wigner-Ville distribution, the discrete ambiguity function and the discrete Gabor transform is shown to be AT/sup 2/= Omega (N/sup 3/ log/sup 2/ N), where N/sup 2/ is the number of output points. The lower bound on multiplicative complexity for these is shown to be Omega (N/sup 2/). For the N-point discrete wavelet transform a lower bound of AT/sup 2/= Omega (N/sup 2/ log/sup 2/ N) and a multiplicative complexity of Omega (N) are the same as the lower bounds for the DFT.<>
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