{"title":"Time Frequency Split Zak Transform for Finite Gabor Expansion","authors":"S. Pei, M. Yeh","doi":"10.1109/ISCAS.1995.523783","DOIUrl":null,"url":null,"abstract":"The relationship between the finite discrete Zak transform and the finite Gabor expansion are discussed in this paper. We present two DFT-based algorithms for computing Gabor coefficients. One is based upon the time-split Zak transform, the other upon the frequency-split Zak transform. These two methods are time and frequency dual pairs. Furthermore, we extend the relationship between the finite discrete Zak transform and the Gabor expansion to the 2-D case and compute 2-D Gabor expansion coefficients through the 2-D discrete Zak transform and 4-D DFT. Four methods can be applied in the 2-D case. They are time-time-split, time-frequency-split, frequency-time-split and frequency-frequency-split.","PeriodicalId":91083,"journal":{"name":"IEEE International Symposium on Circuits and Systems proceedings. IEEE International Symposium on Circuits and Systems","volume":"26 1","pages":"1876-1879"},"PeriodicalIF":0.0000,"publicationDate":"1995-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE International Symposium on Circuits and Systems proceedings. IEEE International Symposium on Circuits and Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISCAS.1995.523783","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
The relationship between the finite discrete Zak transform and the finite Gabor expansion are discussed in this paper. We present two DFT-based algorithms for computing Gabor coefficients. One is based upon the time-split Zak transform, the other upon the frequency-split Zak transform. These two methods are time and frequency dual pairs. Furthermore, we extend the relationship between the finite discrete Zak transform and the Gabor expansion to the 2-D case and compute 2-D Gabor expansion coefficients through the 2-D discrete Zak transform and 4-D DFT. Four methods can be applied in the 2-D case. They are time-time-split, time-frequency-split, frequency-time-split and frequency-frequency-split.