{"title":"Transform Methods","authors":"Wu-Sheng Lu, A. Antoniou","doi":"10.1201/9781003066637-3","DOIUrl":"https://doi.org/10.1201/9781003066637-3","url":null,"abstract":"In this second lecture we discuss the Discrete Fourier Transform (DFT), and its relation to filtering and convolution. Both signals and images will be considered. Applications to deblur-ring and digital image correlation will be discussed. Most of the discussion can be found in greater detail in the reference [1] A good starting point for this discussion is the well-known exponential Fourier series expansion of a function, x(t), on [0, 1]. x(t) = ∞ k=−∞ c k e k (t) = ∞ k=−∞ c k e 2πikt. (1) The Fourier coefficients can be obtained by scalar products: c k = x(t), e k (t) = 1 0 x(t)e 2πikt dt. (2) Now, in a typical sampling situation, we sample x(t) at the N points 0, 1 N , 2 N ,. .. , N − 1 N. to create a vector X = x(0) x(","PeriodicalId":314665,"journal":{"name":"Two-Dimensional Digital Filters","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114260815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite Wordlength Effects","authors":"Wu-Sheng Lu, A. Antoniou","doi":"10.1201/9781003066637-11","DOIUrl":"https://doi.org/10.1201/9781003066637-11","url":null,"abstract":"","PeriodicalId":314665,"journal":{"name":"Two-Dimensional Digital Filters","volume":"515 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123083283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fundamentals","authors":"Wu-Sheng Lu, A. Antoniou","doi":"10.1201/9781003066637-1","DOIUrl":"https://doi.org/10.1201/9781003066637-1","url":null,"abstract":"","PeriodicalId":314665,"journal":{"name":"Two-Dimensional Digital Filters","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122004419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stability Analysis","authors":"Wu Lu, A. Antoniou","doi":"10.1201/9781003066637-5","DOIUrl":"https://doi.org/10.1201/9781003066637-5","url":null,"abstract":"","PeriodicalId":314665,"journal":{"name":"Two-Dimensional Digital Filters","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133033249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Design of Nonrecursive Filters by Optimization","authors":"Wu-Sheng Lu, A. Antoniou","doi":"10.1201/9781003066637-9","DOIUrl":"https://doi.org/10.1201/9781003066637-9","url":null,"abstract":"","PeriodicalId":314665,"journal":{"name":"Two-Dimensional Digital Filters","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122969627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Implementation","authors":"Wu-Sheng Lu, A. Antoniou","doi":"10.1201/9781003066637-12","DOIUrl":"https://doi.org/10.1201/9781003066637-12","url":null,"abstract":"","PeriodicalId":314665,"journal":{"name":"Two-Dimensional Digital Filters","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121013236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Applications","authors":"Wu-Sheng Lu, A. Antoniou","doi":"10.1201/9781003066637-13","DOIUrl":"https://doi.org/10.1201/9781003066637-13","url":null,"abstract":"","PeriodicalId":314665,"journal":{"name":"Two-Dimensional Digital Filters","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130609985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Realization","authors":"Wu-Sheng Lu, A. Antoniou","doi":"10.1201/9781003066637-10","DOIUrl":"https://doi.org/10.1201/9781003066637-10","url":null,"abstract":"","PeriodicalId":314665,"journal":{"name":"Two-Dimensional Digital Filters","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132567797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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