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Parks, Thomas W. Merchant, Gulamabbas A. 2018-12-18T21:22:22Z 2018-12-18T21:22:22Z 1978 Merchant, Gulamabbas A.. "Fast algorithms for DFT and convolution." (1978) Master’s Thesis, Rice University. https://hdl.handle.net/1911/104397. https://hdl.handle.net/1911/104397 RICE2032 THESIS E.E. 1978 MERCHANT Text includes handwritten formulas 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. The algorithms have been Implemented In FORTRAN on IBM 37/155 and their execution timings have been compared. 132 pp reformatted digital eng Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. Fast algorithms for DFT and convolution Thesis Text Electrical Engineering Engineering Rice University Masters Master of Science open.access