{"id":{"repo_id":"rice","oai_identifier":"oai:repository.rice.edu:1911/104397"},"canonical_url":"https://search.dev.ndltd.org/etd/rice/oai:repository.rice.edu:1911/104397","repository":{"repo_id":"rice","name":"Rice University","base_url":"https://repository.rice.edu/server/oai/request"},"display":{"title":"Fast algorithms for DFT and convolution","abstract":"In this thesis, a detailed analysis of sufficient conditions for existence of unique multidimensional linear and multidimensional non-linear Index map has been presented, along with a new Index representation. The recent Ideas of converting Discrete Fourier Transform to convolution and Implementing convolution efficiently, have been combined to give two algorithms viz. Nested Fourier Algorithm (NFA -- using linear multidimensional map) and Index Fourier Algorithm (IFA using a non-linear Index map). The two algorithms have been compared for the amount of arithmetic computations required. 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Nested Fourier Algorithm (NFA -- using linear multidimensional map) and Index Fourier Algorithm (IFA using a non-linear Index map). The two algorithms have been compared for the amount of arithmetic computations required. The algorithms have been Implemented In FORTRAN on IBM 37/155 and their execution timings have been compared."]},{"key":"dc:title","label":"Title","values":["Fast algorithms for DFT and convolution"]}]}],"canonical_facts":{"dc:contributor.advisor":["Parks, Thomas W."],"dc:creator":["Merchant, Gulamabbas A."],"dc:date.accessioned":["2018-12-18T21:22:22Z"],"dc:date.available":["2018-12-18T21:22:22Z"],"dc:date.issued":["1978"],"dc:description":["Text includes handwritten formulas"],"dc:description.abstract":["In this thesis, a detailed analysis of sufficient conditions for existence of unique multidimensional linear and multidimensional non-linear Index map has been presented, along with a new Index representation. 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