{"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}
引用次数: 7
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.<>
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