{"title":"Time-frequency representations for nonlinear frequency scales — Coorbit spaces and discretization","authors":"N. Holighaus, P. Balázs, Christoph Wiesmeyr","doi":"10.1109/SAMPTA.2015.7148865","DOIUrl":null,"url":null,"abstract":"The fixed time-frequency resolution of the short-time Fourier transform has often been considered a major drawback. In this contribution we review recent results on a class of time-frequency transforms that adapt to a large class of frequency scales in the same sense that wavelet transforms are adapted to a logarithmic scale. In particular, we show that each transform in this class of warped time-frequency representations is a tight continuous frame satisfying orthogonality relations similar to Moyal's formula. Moreover, they satisfy the prerequisites of generalized coorbit theory, giving rise to coorbit spaces and associated discrete representations, i.e. atomic decompositions and Banach frames.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 International Conference on Sampling Theory and Applications (SampTA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SAMPTA.2015.7148865","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
The fixed time-frequency resolution of the short-time Fourier transform has often been considered a major drawback. In this contribution we review recent results on a class of time-frequency transforms that adapt to a large class of frequency scales in the same sense that wavelet transforms are adapted to a logarithmic scale. In particular, we show that each transform in this class of warped time-frequency representations is a tight continuous frame satisfying orthogonality relations similar to Moyal's formula. Moreover, they satisfy the prerequisites of generalized coorbit theory, giving rise to coorbit spaces and associated discrete representations, i.e. atomic decompositions and Banach frames.