{"title":"四元数傅里叶变换三种定义之间的关系及反演公式","authors":"M. Bahri, R. Ashino","doi":"10.1109/ICWAPR48189.2019.8946455","DOIUrl":null,"url":null,"abstract":"Firstly, based on basic properties of the kernel function of the quaternion Fourier transform we derive in detail relationships among three definitions of the quaternion Fourier transforms. Secondly, based on the quaternion Fourier transform of the quaternion Gaussian function we derive an inversion formula to recovering a quaternion function from the quaternion Fourier transform.","PeriodicalId":436840,"journal":{"name":"2019 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Relationship Among Three Definitions Of Quaternion Fourier Transforms And Inversion Formula\",\"authors\":\"M. Bahri, R. Ashino\",\"doi\":\"10.1109/ICWAPR48189.2019.8946455\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Firstly, based on basic properties of the kernel function of the quaternion Fourier transform we derive in detail relationships among three definitions of the quaternion Fourier transforms. Secondly, based on the quaternion Fourier transform of the quaternion Gaussian function we derive an inversion formula to recovering a quaternion function from the quaternion Fourier transform.\",\"PeriodicalId\":436840,\"journal\":{\"name\":\"2019 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2019 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICWAPR48189.2019.8946455\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICWAPR48189.2019.8946455","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Relationship Among Three Definitions Of Quaternion Fourier Transforms And Inversion Formula
Firstly, based on basic properties of the kernel function of the quaternion Fourier transform we derive in detail relationships among three definitions of the quaternion Fourier transforms. Secondly, based on the quaternion Fourier transform of the quaternion Gaussian function we derive an inversion formula to recovering a quaternion function from the quaternion Fourier transform.
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